Question

24. A ray of light incidents at an angle of incidence 60° on a refracting surface. If the reflected and
refracted rays are perpendicular to each other, the refractive index of the medium is
​

Answer 1

AnswEr :

• The refractive index of the glass will be √3 = 1.732.

Given :

• A ray of light strikes a glass plate at an angle of 60° with the glass surface.

• The reflected and refracted rays are perpendicular to each other.

To Find :

• Refractive index of the medium = ?

Explanation :

As reflected and refracted rays are perpendicular to each other,

• Angle of incidence = sin 60°
• Angle of refraction = sin 30°

So,

★ Refractive index of the medium :

➝ sin i / sin r

➝ sin 60°/ sin 30°

➝ (√3/2) / (1/2)

➝ √3

➝ 1.732

$\therefore$ The refractive index of the glass will be 1.732

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Something Interesting :

★ Refractive index is the dimensionless number.

★ It is all about the speed of light .

★ Refractive index are of 2 types :

• Relative refractive index.
• Absolute refractive index.

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Answer 2

Answer:

The refractive index of the medium is equal to 1.73.

Explanation:

Given:  

The angle of incidence, $i=60^{o}$

We know that  angle of reflection will be same as angle of incidence .

Therefore the angle of reflection $=60^{o}$

Therefore the angle of reflected ray with surface $=90^{o}-60^{o}=30^{o}$

Given, the reflected ray is perpendicular to the refracted ray. (see attached figure)

Therefore the angle of refraction $r=90^{o}-30^{o}=60^{o}$

Refractive index, $\mu=\frac{Sini}{Sin r}$

⇒     $\mu=\frac{Sin60^{o}}{Sin30^{o}}$

⇒     $\mu =\frac{\sqrt{3} }{2}*2$

∴     $\mu=\sqrt{3}=1.73$

Therefore, the refractive index is 1.73.