Question 402: Ray Optics

Question

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the below figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

Accepted Answer

In $$\Delta$$SAB
$$	an 	heta  = {{AB} \over {AS}} = {{11.54/2} \over {10}}$$
tan$$	heta$$ = 0.577
$$	heta$$ = 30$$^\circ$$
Using $${{\sin {	heta _l}} \over {\sin 90}} = {{{n_l}} \over {{n_B}}}$$, we get
$$\sin {	heta _l} = {{{n_l}} \over {{n_B}}}$$ or $${n_l} = {n_B} 	imes \sin 30 = 2.72 	imes {1 \over 2} = 1.36$$

Answer

1.21

Answer

1.30

Answer

1.36

Answer

1.42

Ray Optics

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