Geometrical Optics — JEE Main PYQs

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be:

In figure, the optical fiber is $l=2\mathrm{m}$ long and has a diameter of $d=20\mu \mathrm{m}$. If a ray of light is incident on one end of the fiber at angle ${\theta }_1=40^{\circ }$, the number of reflection it makes before emerging from the other end is close to:

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, …

Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star.

A concave mirror for face viewing has focal length of 0.4 m . The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is $\sqrt{3}$, then the angle of incidence

A concave mirror has radius of curvature of 40 cm . It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance $d$ from the surface of …

The graph shows how the magnification m produced by a thin lens varies with image distance $v$. What is the focal length of the lens used?

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following, graph is the correct one, if ${\mathrm{D}}_{\mathrm{m}}$ is the angle of minimum deviation?

An object is at a distance of 20 m from a convex lens of focal length 0.3 m . The lens forms an image of the object. If the object moves away from the lens at a speed of 5 $\mathrm{m}/\mathrm{s}$, the speed and direction of the image will be:

What is the position and nature of image formed by lens combination shown in figure? (${\mathrm{f}}_1,{\mathrm{f}}_2$ are focal lengths)

A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2 L as shown below. The distance over which the man …

A transparent cube of side d , made of a material of refractive index ${\mu }_2$, is immersed in a liquid of refractive index ${\mu }_1\left({\mu }_1<{\mu }_2\right)$. A ray is incident on the face $AB$ at an angle $q$ (shown in the figure). Total internal reflection takes p …

A plano-convex lens (focal length $f_2$, refractive index ${\mu }_2$, radius of curvature $R$) fits exactly into a plano-concave lens (focal length ${\mathrm{f}}_1$, refractive index ${\mu }_1$, radius of curvature R). Their plane surfaces are parallel to each other. Th …

Formation of real image using a biconvex lens is shown below :

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

A thin convex lens $L$ (refractive index $=1.5$) is placed on a plane mirror $M$. When a pin is placed at A, such that $\mathrm{OA}=18\mathrm{cm}$, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index ${\mu }_1$ is put between the …

A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances ${\mathrm{x}}_1$ and ${\mathrm{x}}_2\left({\mathrm{x}}_1>{\mathrm{x}}_2\right)$ from the lens. The ratio of ${\mathrm{x}}_1$ and ${\mathrm{x}}_2$ is:

Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror ( $M_1$ ) and parallel to the second mirror ( $M_2$ ) is finally reflected from the second mirror ( ${\mathrm{M}}_2$ ) parallel to the first mirror ( ${\mathrm{M}}_1$ ). …

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a dista …

A ray of light AO in vacuum is incident on a glass slab at angle $60^{\circ }$ and refracted at angle $30^{\circ }$ along OB as shown in the figure. The optical path length of light ray from $A$ to $B$ is:

One plano-convex and one plano-concave lens of same radius of curvature ' R ' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is ${\mu }_1$ and that of 2 is ${\mu }_2$, then the focal length of the combinat …

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is :

An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears :

In an experiment for determination of refractive index of glass of a prism by $\mathrm{i}-\delta$, plot, it was found that a ray incident at angle $35^{\circ }$, suffers a deviation of $40^{\circ }$ and that it emerges at angle $79^{\circ }$. In that case which of the follow …

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$, a ray, incident at an angle $\theta$, on the face AB would get transmitted through the face AC of the prism provided:

A thin convex lens made from crown glass $\left(\mu =\frac{3}{2}\right)$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation betw …

A green light is incident from the water to the air-water interface at the critical angle ($\theta$). Select the correct statement

The graph between angle of deviation ( $\delta$ ) and angle of incidence (i) for a triangular prism is represented by:

Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm . If speed of light in material of lens is $2\times 10^8\mathrm{m}/\mathrm{s}$, the focal length of the lens is :

An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sha …

Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z\ge 0$ has a refractive index of $\sqrt{2}$ and medium 2 with $z<0$ has a refractive index of $\sqrt{3}$. A ray of light in medium 1 given by the vector …

A car is fitted with a convex side-view mirror of focal length 20 cm . A second car 2.8 m behind the first car is overtaking the first car at relative speed of $15\mathrm{m}/\mathrm{s}$. The speed of the image of the second car as seen in the mirror of the first one is :

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v$, from the lens, …

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the …

A student measures the focal length of convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance ' $v$ ' of the image pin. The graph between ' $u$ ' and ' $v$ ' plotted by the student should look like

Two lenses of power -15 D and +5 D are in contact with each other. The focal length of the combination is

The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let $D_1$ and $D_2$ be an of minimum deviation for red and blue light respectively in a prism of this glass. Then

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $4/3$ and the fish is 12 cm below the surface, the radius of this circle in cm is

A light ray is incident perpendicular to one face of a $90^{\circ }$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^{\circ }$, we conclude that the refractive index $n$

A plane convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object?