Geometrical Optics — CBSE Class 12 board PYQs

The focal lengths of the objective and the eyepiece of a compound microscope are $1\mathrm{cm}$ and $2\mathrm{cm}$ respectively. If the tube length of the microscope is $10\mathrm{cm}$, the magnification obtained by the microscope for most suitable viewing by a relaxed eye …

\textbf{Case study (prism and total internal reflection):} A ray of light suffers successive refractions on passing through the two faces of a prism; $\mu =\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \frac{A}{2}}$. If the angle of incidence on the second surface exceeds th …

When a ray of light of wavelength $\lambda$ and frequency $\nu$ is refracted into a denser medium:

The critical angle for a ray of light passing from glass to water is minimum for:

Three beams of red, yellow and violet colours are passed through a prism, one by one, under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are $r_R,r_Y$ and $r_V$ respectively. Then:

A ray of light is incident normally on a prism $ABC$ of refractive index $\sqrt{2}$, as shown in the figure. After it strikes face $AC$, it will:

A beam of light travels from air into a medium. Its speed and wavelength in the medium are $1.5\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$ and $230\mathrm{nm}$ respectively. The wavelength of light in air will be:

\textbf{Case study (total internal reflection):} When a ray travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle, it is totally internally reflected. — A ray of light travels from a medium into water at an angle of incidence of …

A point source of light is placed at the bottom of a tank filled with water of refractive index $\mu$ to a depth $d$. The area of the surface of water through which light from the source can emerge is:

For which of the following media, with respect to air, is the value of the critical angle maximum?

The critical angle for a pair of two media $A$ and $B$ of refractive indices $2.0$ and $1.0$ respectively is:

The critical angle for a pair of a medium and air is $30^{\circ }$. The speed of light in the medium is:

Larger aperture of the objective lens in an astronomical telescope:

A biconvex lens of glass having refractive index $1.47$ is immersed in a liquid. It becomes invisible and behaves as a plane glass plate. The refractive index of the liquid is:

For a glass prism, the angle of minimum deviation will be smallest for the light of:

A ray of light on passing through an equilateral glass prism suffers a minimum deviation equal to the angle of the prism. The value of the refractive index of the material of the prism is \underline{\hspace{2cm}}.

An object is kept in front of a concave lens. What is the nature of the image formed?

When light travels from a rarer medium to a denser medium, the speed of light decreases. Does the reduction in speed imply a reduction in the energy carried by the light?

Why can we not see clearly through fog? Name the phenomenon responsible for it.

A concave lens of refractive index $1.5$ is immersed in a medium of refractive index $1.65$. What is the nature of the lens?

A biconcave lens made of a transparent material of refractive index $1.25$ is immersed in water of refractive index $1.33$. Will the lens behave as a converging or a diverging lens? Give reason.

Under what condition does a biconvex lens of glass having a certain refractive index act as a plane glass sheet when immersed in a liquid?

Calculate the speed of light in a medium whose critical angle is $30^{\circ }$.

A glass lens of refractive index $1.45$ disappears when immersed in a liquid. What is the value of the refractive index of the liquid?

You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope? (Lens $L_1$: power $3\mathrm{D}$, aperture $8\mathrm{cm}$; $L_2$: $6\mathrm{D}$, $1\mathrm{cm}$; $L_3$: …

Two thin lenses of power $+4\mathrm{D}$ and $-2\mathrm{D}$ are in contact. What is the focal length of the combination?

An object is held at the principal focus of a concave lens of focal length $F$. Where is the image formed?

What is the geometrical shape of the wavefront when a plane wavefront passes through a convex lens?

An object is placed at the focus of a concave lens. Where will its image be formed?

A lens of glass is immersed in water. What will be its effect on the power of the lens?

The radius of curvature of a convex mirror is $30\mathrm{cm}$. It forms an image of an object which is half the size of the object. Find the separation between the object and the image.

In the given figure the radius of curvature of the curved face in the plano-convex and the plano-concave lens is $15\mathrm{cm}$ each, and the two lenses (kept $20\mathrm{cm}$ apart) are made of material of refractive index $1.5$. A parallel beam is incident on the combinatio …

Define the critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and the refractive index of the medium.

With the help of a ray diagram, explain the working of a reflecting telescope. Mention two advantages of a reflecting telescope over a refracting telescope.

(A) (i) Define the S.I. unit of power of a lens. (ii) A plano-convex lens is made of glass of refractive index $1.5$. The radius of curvature of the convex surface is $25\mathrm{cm}$. (ii.i) Calculate the focal length of the lens. (ii.ii) If an object is placed …

A ray of light passes through a prism of refractive index $\sqrt{2}$ as shown in the figure. Find
(i) the angle of incidence $(\angle r_2)$ at face $AC$,
(ii) the angle of minimum deviation for this prism.

Using the lens maker's formula, derive the thin lens formula $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ for a biconvex lens.

Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length $15$ m and an eyepiece of focal length $1.0$ cm. If this telescope is used to view the Moon, find t …

(a) Show, using a proper diagram, how unpolarised light can be linearly polarised by reflection from a transparent glass surface.
(b) The figure shows a ray of light falling normally on the face $AB$ of an equilateral glass prism having refractive index $\frac{3}{2}$, placed in …

A symmetric biconvex lens of radius of curvature $R$ and made of glass of refractive index $1.5$ is placed on a layer of liquid placed on top of a plane mirror as shown in the figure. An optical needle with its tip on the principal axis of the lens is moved along the axis until i …

A small illuminated bulb is at the bottom of a tank containing a liquid of refractive index $\mu$ up to a height $H$. Find the expression for the diameter of an opaque disc, floating symmetrically on the liquid surface, in order to cut off the light from the bulb.

A ray of light is incident on a glass prism of refractive index $\mu$ and refracting angle $A$. If it just suffers total internal reflection at the other face, obtain an expression relating the angle of incidence, angle of prism and critical angle.

Why should the objective of a telescope have a large focal length and a large aperture? Justify your answer.

An optical instrument uses an eye-lens of power $16\mathrm{D}$ and an objective lens of power $50\mathrm{D}$, and has a tube length of $16.25\mathrm{cm}$. Name the optical instrument and calculate its magnifying power if it forms the final image at infinity.

(i) A ray of light incident on face $AB$ of an equilateral glass prism shows a minimum deviation of $30^{\circ }$. Calculate the speed of light through the prism.
(ii) Find the angle of incidence at face $AB$ so that the emergent ray grazes along the face $AC$.

A ray $PQ$ incident on the refracting face $BA$ is refracted in the prism $BAC$ as shown in the figure and emerges from the other refracting face $AC$ as $RS$ such that $AQ=AR$. If the angle of prism $A=60^{\circ }$ and the refractive index of the material of the prism is …

(i) A screen is placed at a distance of $100\mathrm{cm}$ from an object. The image of the object is formed on the screen by a convex lens for two different positions of the lens separated by $20\mathrm{cm}$. Calculate the focal length of the lens used.
(ii) A converging lens …

(a) Calculate the distance of an object of height $h$ from a concave mirror of radius of curvature $20\mathrm{cm}$, so as to obtain a real image of magnification $2$. Find the location of the image also.
(b) Using the mirror formula, explain why a convex mirror always produces …

Draw a schematic ray diagram of a reflecting telescope showing how rays coming from a distant object are received at the eyepiece. Write its two important advantages over a refracting telescope.

Use the mirror equation to show that an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.

(i) A giant refracting telescope has an objective lens of focal length $15\mathrm{m}$. If an eyepiece of focal length $1.0\mathrm{cm}$ is used, what is the angular magnification of the telescope?
(ii) If this telescope is used to view the Moon, what is the diameter of the ima …

Two monochromatic rays of light are incident normally on the face $AB$ of an isosceles right-angled prism $ABC$. The refractive indices of the glass prism for the two rays `1' and `2' are respectively $1.38$ and $1.52$. Trace the path of these rays after entering through the pris …

A convex lens of focal length $20\mathrm{cm}$ is placed coaxially with a convex mirror of radius of curvature $20\mathrm{cm}$. The two are kept $15\mathrm{cm}$ apart. A point object is placed $40\mathrm{cm}$ in front of the convex lens. Find the position of the image form …

A convex lens of focal length $f_1$ is kept in contact with a concave lens of focal length $f_2$. Find the focal length of the combination.

Draw a labelled ray diagram of a refracting telescope. Define its magnifying power and write the expression for it. Write two important limitations of a refracting telescope over a reflecting type telescope.

A ray of light, incident on an equilateral prism $(\mu =\sqrt{3})$, moves parallel to the base line of the prism inside it. Find the angle of incidence for this ray.

A convex lens made up of glass of refractive index $1.5$ is dipped, in turn, in (i) a medium of refractive index $1.33$, (ii) a medium of refractive index $1.65$. (a) Will it behave as a converging or a diverging lens in the two cases? (b) How will its focal length change in the …

Find the radius of curvature of the convex surface of a plano-convex lens, whose focal length is $0.3\mathrm{m}$ and the refractive index of the material of the lens is $1.5$.

(i) Out of blue and red light, which is deviated more by a prism? Give reason.
(ii) Give the formula that can be used to determine the refractive index of the material of a prism in the minimum deviation condition.

Three light rays red (R), green (G) and blue (B) are incident on a right-angled prism `abc' at face `ab'. The refractive indices of the material of the prism for red, green and blue wavelengths are $1.39$, $1.44$ and $1.47$ respectively. Out of the three, which colour ray will em …

In the figure, light rays of blue, green and red wavelengths are incident on an isosceles right-angled prism. Explain, with reason, which ray of light will be transmitted through the face $AC$. The refractive indices of the prism for red, green and blue light are $1.39$, $1.424$ …

Draw a plot showing the variation of power of a lens with the wavelength of the incident light. A diverging lens of refractive index $1.5$ and of focal length $20\mathrm{cm}$ in air has the same radii of curvature for both sides. If it is immersed in a liquid of refractive inde …

A convex lens of refractive index $1.5$ has a focal length of $18\mathrm{cm}$ in air. Calculate the change in its focal length when it is immersed in water of refractive index $\frac{4}{3}$.

Define the term `resolving power' of an astronomical telescope. How does it get affected on
(i) increasing the aperture of the objective lens,
(ii) increasing the wavelength of the light used? Justify your answer in each case.

Draw a labelled ray diagram of a reflecting type telescope. Write any one advantage it has over a refracting type telescope.

A beam of light converges to a point $P$. A lens is placed in the path of the convergent beam $12\mathrm{cm}$ from $P$. At what point does the beam converge if the lens is
(i) a convex lens of focal length $20\mathrm{cm}$,
(ii) a concave lens of focal length $16\mathrm{cm}$ …

A convex lens made up of glass of refractive index $1.5$ is dipped, in turn, in
(i) medium $A$ of refractive index $1.65$,
(ii) medium $B$ of refractive index $1.33$. Explain, giving reasons, whether it will behave as a converging lens or a diverging lens in each of these two med …

A right-angled crown glass prism with critical angle $41^{\circ }$ is placed before an object $PQ$ in two positions as shown in the figures
(i) and
(ii). Trace the paths of the rays from $P$ and $Q$ passing through the prisms in the two cases.

(a) Draw a labelled ray diagram to show the formation of an image by a compound microscope. Write the expression for its magnifying power. (b) How does the resolving power of a compound microscope change when (i) the refractive index of the medium between the object and the objec …

A double convex lens made of glass of refractive index $1.6$ has both surfaces of equal radii of curvature of $30\mathrm{cm}$ each. An object of $5\mathrm{cm}$ height is placed at a distance of $12.5\mathrm{cm}$ from the lens. Find the position, nature and size of the image …

A double convex lens made of glass of refractive index $1.5$ has both surfaces of equal radii of curvature of $20\mathrm{cm}$ each. An object of $5\mathrm{cm}$ height is placed at a distance of $10\mathrm{cm}$ from the lens. Find the position, nature and size of the image.

A figure divided into squares, each of size $1{\mathrm{mm}}^2$, is being viewed at a distance of $9\mathrm{cm}$ through a magnifying lens of focal length $10\mathrm{cm}$, held close to the eye.
(a) Draw a ray diagram showing the formation of the image.
(b) What is the magni …

Define critical angle with reference to total internal reflection. Calculate the critical angle for a glass--air surface, if a ray of light which is incident in air on the glass surface is deviated through $15^{\circ }$ when the angle of incidence is $45^{\circ }$.

A converging lens of focal length $6.25\mathrm{cm}$ is used as a magnifying glass. If the near point of the observer is $25\mathrm{cm}$ from the eye and the lens is held close to the eye, calculate
(i) the distance of the object from the lens,
(ii) the angular magnification ( …

The image of a candle is formed by a convex lens on a screen. The lower half of the lens is painted black so as to be completely opaque. What will be the effect on the image formed?

(a) (i) State Huygens' principle. With the help of a diagram, show how a plane wave is reflected from a surface and hence verify the law of reflection. (ii) A concave mirror of focal length $12\mathrm{cm}$ forms a three times magnified virtual image of an object. Find the dista …

(a) Draw the ray diagram of an astronomical telescope when the final image is formed at infinity. Write the expression for the resolving power of the telescope. (b) An astronomical telescope has an objective lens of focal length $20\mathrm{m}$ and an eyepiece of focal length …

(a) With a suitable ray diagram, derive the mirror formula $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ for a spherical mirror.
(b) A plano-convex lens of radius of curvature $20\mathrm{cm}$ is made of glass of refractive index $1.5$. According to the lens maker's formula, find its …

(a) Under what conditions is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.
(b) Three lenses of focal lengths $+10$ cm, $-10$ cm and $+30$ cm are arranged coaxially …

(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.
(b) Obtain the mirror formula and write the expression for the linear magnification.
(c) Explain two advantages of a reflecting telescope over a ref …

Mrs. Rashmi Singh broke her reading glasses. When she went to the shopkeeper to order new spectacles, he suggested that she should get spectacles with plastic lenses instead of glass lenses. On getting the new spectacles, she found that the new ones were thicker than the earlier …

(a) Plot a graph to show the variation of the angle of deviation as a function of the angle of incidence for light passing through a prism. Derive an expression for the refractive index of the prism in terms of the angle of minimum deviation and the angle of the prism.
(b) What i …

(a) A point object `O' is kept in a medium of refractive index $n_1$ in front of a convex spherical surface of radius of curvature $R$ which separates a second medium of refractive index $n_2$ from the first one, as shown in the figure. Draw the ray diagram showing the image …

Define the magnifying power of a telescope. Write its expression. A small telescope has an objective lens of focal length $150\mathrm{cm}$ and an eyepiece of focal length $5\mathrm{cm}$. If this telescope is used to view a $100\mathrm{m}$ high tower $3\mathrm{km}$ away, f …

How is the working of a telescope different from that of a microscope? The focal lengths of the objective and eyepiece of a microscope are $1.25\mathrm{cm}$ and $5\mathrm{cm}$ respectively. Find the position of the object relative to the objective in order to obtain an angula …

A compound microscope uses an objective lens of focal length $4\mathrm{cm}$ and an eyepiece lens of focal length $10\mathrm{cm}$. An object is placed at $6\mathrm{cm}$ from the objective lens. Calculate the magnifying power of the compound microscope when the final image is …

A giant refracting telescope at an observatory has an objective lens of focal length $15\mathrm{m}$. If an eyepiece lens of focal length $1.0\mathrm{cm}$ is used, find the angular magnification of the telescope. If this telescope is used to view the Moon, what is the diameter …

Draw a ray diagram to show the working of a compound microscope. Deduce an expression for the total magnification when the final image is formed at the near point. In a compound microscope, an object is placed at a distance of $1.5\mathrm{cm}$ from the objective of focal length …

(a) (i) Draw a labelled ray diagram to show the formation of an image in an astronomical telescope for a distant object. (ii) Write three distinct advantages of a reflecting type telescope over a refracting type telescope. (b) A convex lens of focal length $10\mathrm{cm}$ is pl …

(a) With the help of a suitable ray diagram, derive the mirror formula for a concave mirror.
(b) The near point of a hypermetropic person is $50\mathrm{cm}$ from the eye. What is the power of the lens required to enable the person to read clearly a book held at …

Trace the rays of light showing the formation of an image due to a point object placed on the axis of a spherical surface separating two media of refractive indices $n_1$ and $n_2$. Establish the relation between the distances of the object, the image and the radius of curvat …

Draw the labelled ray diagram for the formation of an image by a compound microscope. Derive the expression for the total magnification of a compound microscope. Explain why both the objective and the eyepiece of a compound microscope must have short focal lengths.

Draw a labelled ray diagram of a compound microscope and write an expression for its magnifying power. The focal lengths of the objective and eye-lens of a compound microscope are $2\mathrm{cm}$ and $6.25\mathrm{cm}$ respectively. The distance between the lenses is …