A ray of light traveling in water is incident on its surface open to air. The angle of incidence is $\theta$, which is less than the critical angle. Then there will be

(C) a reflected ray and a refracted ray and the angle between them would be less than $180^{\circ}-2 \theta$

(A) only a reflected ray and no refracted ray

(B) only a refracted ray and no reflected ray

(D) a reflected ray and a refracted ray and the angle between them would be greater than $180^{\circ}-2 \theta$

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Geometrical Optics

A ray of light traveling in water is incident on its surface open to air. The angle of incidence is

θ

, which is less than the critical angle. Then there will be

(A)only a reflected ray and no refracted ray
(B)only a refracted ray and no reflected ray
(C)a reflected ray and a refracted ray and the angle between them would be less than $18 0^{\circ} - 2 θ$ ✓ Correct
(D)a reflected ray and a refracted ray and the angle between them would be greater than $18 0^{\circ} - 2 θ$

Answer: (C)

Solution

When light travels from a denser medium (water) to a rarer medium (air) at an angle less than the critical angle, both reflection and refraction occur. The reflected ray makes an angle

θ

with the normal on the water side. The refracted ray bends away from the normal, making an angle

r > θ

with the normal on the air side (by Snell's law, since

n_{w a t er} > n_{ai r}

).

The angle between the reflected and refracted rays can be shown geometrically to be less than

18 0^{\circ} - 2 θ

because the refracted ray bends away from the normal.

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Geometrical Optics

Solution

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