Question

Find the lateral shift of light ray while it passes through a parallel glass slab of thickness $10\text{cm}$ placed in air. The angle of incidence in air is ${60}^{\circ }$ and angle of refraction in glass is ${45}^{\circ }$.

• A. $10\sqrt{2}\sin {15}^{\circ }\text{cm}$
• B. $15\sqrt{2}\cos {15}^{\circ }\text{cm}$
  
• C. $10\tan {15}^{\circ }\text{cm}$
• D. $5\sqrt{2}\cos {15}^{\circ }\text{cm}$

Answer 1

The correct option is A $10\sqrt{2}\sin {15}^{\circ }\text{cm}$

Here $t=10\text{cm}$

Applying formula for lateral shift,
$d=t\frac{\sin (i-r)}{\cos r}$

$\Rightarrow d=10\frac{\sin ({60}^{\circ }-{45}^{\circ })}{\cos {45}^{\circ }}$

or,

$d=\frac{10\sin {15}^{\circ }}{\left(\frac{1}{\sqrt{2}}\right)}$

$\therefore d=10\sqrt{2}\sin {15}^{\circ }\text{cm}$

Hence, option (a) is the correct answer.

Why this question? Tip: Remember the formula for lateral shift to save time in exam.