Question

A ray of light strikes a surface and is reflected so that the angle between the incident ray and the reflected ray is 30 degrees. If the surface is rotated so that the angle of incidence is decreased by 1 ˚, what is now the angle between the two rays?​

Answer 1

Answer:

Since angle of incident =angle of reflection

Hence r=30⁰

And here angle of deviation,

δ=180⁰−(i+r)

δ=120

Answer 2

$\large{\underline{\textsf{\textbf{ Given \: Information :}}}}$

• A ray of light strikes a surface and is reflected so that the angle between the incident ray and the reflected ray is 30 degrees.

• If the surface is rotated so that the angle of incidence is decreased by 1˚.

$\large{\underline{\textsf{\textbf{ To \: Calculate :}}}}$

• Angle between two rays after the surface is rotated.

$\large{\underline{\textsf{\textbf{ Calculation :}}}}$

Before the surface is rotated :

• Angle between the incident ray and the reflected ray = 30°

Let's find out the measure of angle of incidence and the angle of reflection before the surface is rotated.

We know that,

According to the laws of reflection,

$\longrightarrow \sf{ \angle i = \angle r}$

• Angle of incidence and angle of reflection are always equal.

So, let's assume the measure each of these two angles as x° for now. (As both's measure are same).

$\longrightarrow \sf { \angle i + \angle r = 30^\circ }$

$\longrightarrow \sf { x^\circ + x^\circ = 30^\circ }$

$\longrightarrow \sf { 2x^\circ = 30^\circ }$

$\longrightarrow \sf { x^\circ = \dfrac{30^\circ }{2} }$

$\longrightarrow \sf { x^\circ = 15^\circ }$

As we have assumed the measure of angle of incidence angle of reflection as x°. So, before the surface is rotated the angle incidence and angle of reflection are :-

$\longrightarrow \sf \red { \angle i= 15^\circ }$

$\longrightarrow \sf \red { \angle r= 15^\circ }$

Now, after rotating the surface :

• After the surface is rotated the angle of incidence is decreased by 1˚.

$\longrightarrow \sf { \angle i= 15^\circ - 1^\circ }$

$\longrightarrow \sf \red { \angle i= 14^\circ }$

The measure of angle of reflection will be also 14° ad because the angle of incidence and angle of reflection are always equal.

$\longrightarrow \sf \red { \angle r= 14^\circ }$

Angle between two rays after the surface is rotated :-

• Angle between two rays = Angle of incidence + Angle of reflection [After rotation]

$\longrightarrow \sf { \angle i + \angle r }$

$\longrightarrow \sf { 14^\circ + 14^\circ }$

$\longrightarrow \boxed{\pmb{ \sf \red{ 28^\circ }}}$

Therefore, angle between two rays after the surface is rotated is 28° .