Question

A ray incident at angle θ on a face PQ of glass slab and passes through the opposite face RS as shown below. d is the lateral displacement of the ray.

If whole system is placed in the water whose refractive index is less than that of glass slab, then the lateral shift (d′)

• A. Will be less than d
• B. Will be greater than d
• C. Will be equal to d
• D. Will become zero

Answer 1

The correct option is A Will be less than d

If we compare the refractive index of air, water and glass, then
${\mu }_{air}<{\mu }_{water}<{\mu }_{glass}$
$\frac{{\mu }_{glass}}{{\mu }_{air}}>\frac{{\mu }_{glass}}{{\mu }_{water}}$
${\left(\frac{\sin i}{\sin r}\right)}_{air-glass}>{\left(\frac{\sin i}{\sin r\text{'}}\right)}_{water-glass}$
sin r' > sin r
$\Rightarrow r^{\prime }>r$ ($\theta <{90}^o$, where $\theta$ is the angle of refract ion)
When the whole system is immersed in water, then the angle of refraction from the first surface increases and hence the lateral displacement decreases [i.e, d′ < d].
Hence, the correct answer is option (a).