Question

A ray of light from a denser medium strikes a rarer medium at an angle of incidence i as shown in the figure. Refracted and reflected rays make an angle of 90° with each other. The angle of reflection and refraction are r and r'. The critical angle is ______.

 

Options

• sin^-1(sin i)

• sin^-1(sin r)

• sin^-1(tan i)

• sin^-1(tan r)

Answer 1

A ray of light from a denser medium strikes a rarer medium at an angle of incidence i as shown in the figure. Refracted and reflected rays make an angle of 90° with each other. The angle of reflection and refraction are r and r'. The critical angle is sin^-1(tan r).

Explanation:

From fig., r + r' = 90°

∴ r' = 90° - r

=  90° - i

When light travels from a denser medium to a rarer medium,

`1/mu = sini/sinr^'`

= `sini/(sin(90^circ - i))`

= `sini/cosi`

= tan i

Also, `sini_c = 1/mu`

(If angle of incidence = critical angle)

∴ `sini_c` = tan i = tan r

∴ i_c = sin^-1(tan r)