Question 365: Ray Optics

Question

A wide slab consisting of two media of refractive indices n
1
and n
2
is placed in air as shown in the figure. A ray of light is incident from medium n
1
to n
2
at an angle $$	heta$$, where sin$$	heta$$ is slightly larger than 1/n
1
. Take refractive index of air as 1. Which of the following statement(s) is(are) correct?

Accepted Answer

$$\sin 	heta  > {1 \over {{n_1}}}$$ (Given)
i.e., $$\sin {	heta _1} > {1 \over {{n_1}}}$$
$${n_1}\sin {	heta _1} = {n_2}\sin {	heta _2}$$
$$\sin {	heta _2} = {{{n_1}\sin {	heta _1}} \over {{n_2}}}$$
if $${n_1} = {n_2}$$ then $${	heta _2} = {	heta _1}$$
$${n_2}\sin {	heta _2} = (1)\sin {	heta _3}$$
$$\sin {	heta _3} = {n_2}\sin {	heta _2}$$
$$\sin {	heta _3} = {n_1}\sin {	heta _1}$$
$$\sin {	heta _1} = {{\sin {	heta _3}} \over {{n_1}}} > {1 \over {{n_1}}}$$
$$\sin {	heta _3} > 1$$
$${	heta _3} > 90^\circ $$
This means ray cannot enter air.
For $${n_1} > {n_2};\sin {	heta _1} = {{{n_2}} \over {{n_1}}}\sin {	heta _2} > {1 \over {{n_1}}}$$
$$\sin {	heta _2} > {1 \over {{n_2}}}$$
For surface 2 - air interface
$${n_2}\sin {	heta _2} = \sin {	heta _3}$$
$$\sin {	heta _2} = {{\sin {	heta _3}} \over {{n_2}}} > {1 \over {{n_2}}}$$
$${	heta _2} > 90^\circ $$
It means ray is reflected back in medium-2
For surface 1 and surface 2 interface
$${n_2}\sin {	heta _2} = {n_1}\sin {	heta _1}$$
$$\sin {	heta _{2C}} = {{{n_1}} \over {{n_2}}}$$
$${	heta _{2C}}$$ : critical angle
For ray to enter medium - 1
$${	heta _2}  {n_1}$$
$${{{n_2}} \over {{n_1}}}\sin {	heta _2} > {{{n_2}} \over {{n_1}}}$$
$$\sin {	heta _2} > {1 \over {{n_2}}}$$
For surface 2 - air interface
$${n_2}\sin {	heta _2} = \sin {	heta _3}$$
$$\sin {	heta _2} = {{\sin {	heta _3}} \over {{n_2}}} > {1 \over {{n_2}}}$$
$${	heta _2} > 90$$
It means ray reflected back in medium - 2
$${n_2}\sin {	heta _2} = {n_1}\sin {	heta _1}$$
$$\sin {	heta _1} = {{{n_2}} \over {{n_1}}}\sin {	heta _2}$$
$$\sin {	heta _{2C}} = {{{n_1}} \over {{n_2}}};{	heta _{2C}}$$ $$	o$$ critical angle
For ray to enter medium - 1
$${	heta _2}  {1 \over {{n_1}}}$$
$$\sin {	heta _2} > 1 \Rightarrow {	heta _2} = 90^\circ $$
$$	herefore$$ Ray is reflected back in medium.

Answer

The light ray enters air if n
2
= n
1

Answer

The light ray is finally reflected back into the medium of refractive index n
1
if n
2
< n
1

Answer

The light ray is finally reflected back into the medium of refractive index n
1
if n
2
> n
1

Answer

The light ray is reflected back into the medium of refractive index n
1
if n
2
= 1

Ray Optics

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