Ncert Exercises & Solutions

9.22 At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.

Hint: Use snell's law.

Step 1: Find the angle of incidence at face AC
Glass prism ABC

The angle of the prism, A= $60 °$
Refractive index of the prism, $μ$ =1.524

At the face AB:
$_{1}$ = Incident angle
$_{1}$ = Refracted angle

At the face AC:
$r_{c}$ = Angle of incidence
e= Emergent angle = $90 °$

For face AC, according to Snell’s law,

$\frac{sine}{{sinr}_{c}} = μ$

Step 2: Find the angle of refraction at face AB.
It is clear from the figure that angle A= $r_{1} + r_{c}$

$∴ r_{1} = A - r_{c} = 60 ° - 41 ° = 19 °$

Step 3: Find the angle of incidence at AB
For surface AB, according to Snell’s law,

$μ = \frac{{sini}_{1}}{{sinr}_{1}}$
${sini}_{1} = {μsinr}_{1} = 1.524 \times \sin 19 ° = 0.496$
$∴ i_{1} = 29.75 °$

Therefore the angle of incidence at the surface AB is $29.75 °.$

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