The principal section of glass prism is an isosceles ΔPQR with PQ = PR. The face PR is silvered. A ray is incident perpendicularly on face PQ, and after two reflections, it emerges from base QR, normal to it. Find the angle (in degree) of the prism.

Open in App

Solution

The angle at second reflection is
$\frac{9 A}{2} + \frac{π}{2} - 2 A = π$
$\frac{5 A}{2} = \frac{π}{2}$
$A = \frac{π}{5} = 36^{o}$

Suggest Corrections

Similar questions

Q. An isosceles glass prism having refractive index

μ

has one of its faces coated with silver. A ray of light is incident normally on the other face(which is equal to the silvered face). The ray of light is reflected twice on the same sized faces and then emerges through the base of the prism perpendicularly. The angles of the prism are:

Q. An isosceles prism has one of the refracting surfaces silvered. A ray of light is incident normally on the refracting face AB. After two reflections, the ray emerges from the base of the prism perpendicular to it. Find the angle of the prism.

Q. The face

P R

of a prism

Q P R

of angle

30^{o}

is silvered. A ray incident on face

P Q

at an angle of

45^{o}

as shown in the figure. The refracted ray undergoes reflected on face

P R

and retraces its path. The refractive index of the prism is

The cross-section of a glass prism has the form of an isosceles triangle. One of the refracting faces is silvered. A ray of light falls normally on the other refracting face. After being reflected twice, it emerges through the base of the prism perpendicular to it. The angles of the prism are

A ray of light incident parallel to the base PQ of an isosceles right-angled triangular prism PQR suffers two successive total internal reflections at the faces PQ and QR before emerging reversed in direction as shown

If the refractive index of the material of the prism is $μ$ , then

Join BYJU'S Learning Program

The principal section of glass prism is an isosceles ΔPQR with PQ = PR. The face PR is silvered. A ray is incident perpendicularly on face PQ, and after two reflections, it emerges from base QR, normal to it. Find the angle (in degree) of the prism.

The angle at second reflection is 9A2+π2−2A=π 5A2=π2 A=π5=36o

The angle at second reflection is
$\frac{9 A}{2} + \frac{π}{2} - 2 A = π$
$\frac{5 A}{2} = \frac{π}{2}$
$A = \frac{π}{5} = 36^{o}$