Name: Total Internal Reflection From Prism
Uploaded: 2019-07-19
Duration: 1 min 56 s
Description: You must have seen reflectors on a bicycle. Why are they attached to the mudguards? What use do they have? Let’s watch this video on reflectors to find out.

Question

Draw a ray diagram to show the refraction of light through a glass prism. Hence, obtain the relation for angle of deviation in terms of angle of incidence, angle of emergence and angle of prism. What is the refractive index of the material of the prism?

Accepted Answer

Consider a ray of light PQ incident on a face AB of a prism as shown. The refracted ray QR again suffers refraction on the second face and emerges as emergent ray RS

$∠ PQN = i, ∠ SRN' = angle of emergence e, ∠ RQO = r_{1} and ∠ QRO = r_{2}$

$and ∠ KTS = δ, angle of deviation$

$∠ T Q R = i - r_{1},$

$∠ T R O = e$ ,

$∠ Q R O = r_{2,},$

Hence, $∠ TRQ = e - r_{2}$

$Exterior angle δ = ∠ TQR + ∠ TRQ = (i - r_{1}) + (e - r_{2}) or δ = (i + e) - (r_{1} + r_{2})$

In $△ QRO ∠ r_{1} + ∠ r_{2} + ∠ QOR = 180^{\circ} \dots (ii)$

In quadrilateral $AQOR,$

$∠ AQO = ∠ ARO = 90^{\circ}$

Hence, $∠ A + ∠ QOR = 180^{\circ} \dots (iii)$

Equating equations (ii) and (iii)

We have $r_{1} + r_{2} = A$

Substituting in the equation

We have

$δ = (i + e) - A$

$\Rightarrow A + δ = i + e$

i.e the sum of the angle of deviation and the angle of the prism is equal to that of the angle of incidence and the angle of emergence.

When the prism is placed in the minimum deviation position,

then $r_{1} = r_{2} = r$ and $i = e$

$∴ A = r_{1} + r_{2} = r + r = 2 r$

and $i + u = A + δ_{m}$

$\Rightarrow 2 i = A + δ_{m}$

Now, $μ = \frac{\sin i}{\sin r} = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}$

Draw a ray diagram to show the refraction of light through a glass prism. Hence, obtain the relation for angle of deviation in terms of angle of incidence, angle of emergence and angle of prism. What is the refractive index of the material of the prism?

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !