CBSE Class 12 · 2024 · Geometrical OpticsMultiple Choice

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\textbf{Case study (prism and total internal reflection):} A ray of light suffers successive refractions on passing through the two faces of a prism;

μ = \frac{sin ( \frac{A + δ _{m}}{2} )}{sin \frac{A}{2}}

. If the angle of incidence on the second surface exceeds the critical angle, the ray is totally internally reflected. — The critical angle for glass is

θ_{1}

and that for water is

θ_{2}

. The critical angle for a glass--water surface would be (given

_{a} μ_{g} = 1.5,_{a} μ_{w} = 1.33

(A)less than $θ_{2}$
(B)between $θ_{1}$ and $θ_{2}$
(C)greater than $θ_{2}$ ✓ Correct
(D)less than $θ_{1}$

Answer: (C)

Solution

Glass

\to

water:

sin θ_{c} = \frac{μ _{w}}{μ _{g}} = \frac{1.33}{1.5} = 0.887 \Rightarrow θ_{c} \approx 62. 5^{\circ}

. Meanwhile

θ_{1}

(glass–air)

= sin^{- 1} \frac{1}{1.5} = 41. 8^{\circ}

and

θ_{2}

(water–air)

= sin^{- 1} \frac{1}{1.33} = 48. 8^{\circ}

. Since

62. 5^{\circ} > 48. 8^{\circ}

, the glass–water critical angle is \emph{greater than}

θ_{2}

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CBSE Class 12 · 2024 · Geometrical OpticsMultiple Choice

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