Question

Lateral displacement of the emergent ray of light increases with,
A. Increase in angle of incidence
B. Decrease in refractive index of medium
C. Increase in the wavelength of light
D. None

Answer 1

Hint: In refraction through a medium, emergent ray is parallel to the incident ray but appears slightly shifted and this shift in the position of the emergent ray, as compared to the incident ray is called Lateral displacement.

Complete step by step answer:
Lateral displacement: The perpendicular distance between the incident ray and the emergent ray is defined as lateral shift. This shift depends upon the angle of incidence, the angle of refraction and the thickness of the medium.

Mathematically, lateral shift is given by,
\[{{S}_{lateral}}=\dfrac{t}{\cos r}\sin (i-r)\]
Where,
\[{{S}_{lateral}}\] = lateral shift
t = thickness of medium
i = angle of incidence
r = angle of refraction

By the above formula we observe that the lateral displacement of the emergent ray of light increases with increase in angle of incidence.
Hence, the correct option is A, i.e., Increase in angle of incidence.

Additional Information:
Refraction occurs when light crosses two boundaries. Basically, a wave front is good representation here, not the ray representation. Ray is just a line drawn perpendicular to the wave front. When a wave front hits the glass at oblique angle, part of the wave enters glass and slows down. Gradually remaining part of the wave front enters glass and slows down. Wave front changes angle just because of entering partly in glass and partly in air.

Note: Students should analyse the factors affecting the lateral displacement by the formula given above i.e., lateral displacement increases with the refractive index of the medium so option B is incorrect and it decreases with the wavelength so option C is also incorrect.