The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\vec{a}, \vec{b}$ and $\vec{c}$ respectively. Then choose the correct relation for these vectors.

(D) $\overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}}-2(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}) \overrightarrow{\mathrm{c}}$

(B) $\vec{b}=\vec{a}+2 \vec{c}$

(C) $\vec{b}=2 \vec{a}+\vec{c}$

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Geometrical Optics

WhatsApp Email

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors

a, b

and

c

respectively. Then choose the correct relation for these vectors.

(A) $b = a - c$
(B) $b = a + 2 c$
(C) $b = 2 a + c$
(D) $b = a - 2 (a \cdot c) c$ ✓ Correct

Answer: (D)

Solution

Split the incident unit vector into a part along the normal and a part lying in the mirror surface. Reflection leaves the surface part untouched and reverses the normal part. The normal part of

a

(a \cdot c) c

, and reversing it means subtracting twice that part from

a

b = a - 2 (a \cdot c) c

This keeps

∣ b ∣ = ∣ a ∣ = 1

and makes the angle with the normal the same on both sides, so the three unit vectors satisfy

b = a - 2 (a \cdot c) c

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Geometrical Optics →

More JEE Main questions on Geometrical Optics

Consider an equilateral prism (refractive index $2$ ). A ray of light is incident on its one surface at a certain angle $i$ . If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ____ .
JEE Main 2026View solution →
A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance x cm from the centre of the curvature of the spherical su …
JEE Main 2026View solution →
In parallax method for the determination of focal length of a concave mirror, the object should always be placed :
JEE Main 2026View solution →
The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is $\frac{4}{3}$ . The wavelength of the same light when it is passing through a transparent medium having refractive index of $\frac{3}{2}$ is $____$ nm.
JEE Main 2026View solution →
As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.

If refractive index of the material of prism is $2$ , the angle $θ$ of prism is.
JEE Main 2026View solution →
A thin prism with angle $5^{\circ}$ of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is ______.
JEE Main 2026View solution →