The lateral shift produced by a glass slab during refraction through it, increases with -
(A) the increase in the thickness of the glass slab
(B) the increase in the value of the angle of incidence
(C) the increase in the value of the refractive index of the slab
(D) the increase in the length of the glass slab
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
For a slab of thickness \( t \), the lateral shift (the sideways distance between the emergent ray and the extended incident ray) is
\( \displaystyle d = \frac{t\,\sin(i - r)}{\cos r} \)
where \( i \) is the angle of incidence and \( r \) the angle of refraction.
(A) the increase in the thickness of the glass slab — Correct. \( d \) is directly proportional to \( t \).
(B) the increase in the value of the angle of incidence — Correct. A larger \( i \) gives a larger \( i - r \), so \( \sin(i-r)/\cos r \) grows.
(C) the increase in the value of the refractive index of the slab — Correct. With \( \sin i = \mu\sin r \), a larger \( \mu \) makes \( r \) smaller, so \( i - r \) is larger and the shift increases.
(D) the increase in the length of the glass slab — Incorrect. The shift depends on the thickness between the two faces; the length along the faces does not appear in the formula.
Statements (A), (B) and (C) are correct, which is Option (2).