A rectangular glass slab A B C D of refractive index μ1, is immersed in water of refractive inde

step 1 For this question, according to Snell's law, Mew 1 divided by Mew 2 is equal to sine, alpha max

A rectangular glass slab A B C D of refractive index μ1, is...

A rectangular glass slab $A B C D$ of refractive index $\mu_{1}$, is immersed in water of refractive index $\mu_{2}\left(\mu_{1}>\mu_{2}\right) . \mathrm{A}$ ray of light is incident at the surface $A B$ of the slab as shown. The maximum value of the angle of incidence $\alpha_{\max }$, such that the ray comes out only from the other surface $C D$ is given by (a) $\sin ^{-1}\left[\left(\frac{\mu_{1}}{\mu_{2}}\right) \cos \left(\sin ^{-1} \frac{\mu_{1}}{\mu_{1}}\right)\right]$ (b) $\sin ^{-1}\left(\frac{\alpha_{2}}{\alpha_{1}}\right)$ (c) $\sin ^{-1}\left[\alpha_{1} \cdot \cos \left(\sin ^{-1} \frac{1}{\alpha_{2}}\right)\right]$ (d) $\left[\sin ^{-1} \frac{\alpha_{1}}{\alpha_{2}}\right]$

A rectangular glass slab $A B C D$ of refractive index $\mu_{1}$, is immersed in water of refractive index $\mu_{2}\left(\mu_{1}>\mu_{2}\right) . \mathrm{A}$ ray of light is incident at the surface $A B$ of the slab as shown. The maximum value of the angle of incidence $\alpha_{\max }$, such that the ray comes out only from the other surface $C D$ is given by
(a) $\sin ^{-1}\left[\left(\frac{\mu_{1}}{\mu_{2}}\right) \cos \left(\sin ^{-1} \frac{\mu_{1}}{\mu_{1}}\right)\right]$
(b) $\sin ^{-1}\left(\frac{\alpha_{2}}{\alpha_{1}}\right)$
(c) $\sin ^{-1}\left[\alpha_{1} \cdot \cos \left(\sin ^{-1} \frac{1}{\alpha_{2}}\right)\right]$
(d) $\left[\sin ^{-1} \frac{\alpha_{1}}{\alpha_{2}}\right]$

Key Concepts

Total Internal Reflection

Total internal reflection is the phenomenon that occurs when a light ray strikes the boundary between a denser and a rarer medium at an angle greater than the critical angle, causing the light to be completely reflected back into the denser medium. Understanding this effect is key when analyzing optical systems that rely on controlled light propagation, such as ensuring that light exits from a specific surface of a slab.

Critical Angle

The critical angle is a specific angle of incidence in the denser medium above which light cannot refract into the less dense medium and instead undergoes total internal reflection. This concept is crucial in determining the maximum angle of incidence for which the light ray can successfully exit the medium along the desired path rather than being trapped by internal reflection.

Refraction and Refractive Index

Refraction is the bending of light as it passes from one medium to another with a different refractive index. The refractive index quantifies how much the light slows down in a medium compared to vacuum. In problems like this, the difference in refractive indices between media is critical in determining the bending of the ray as it enters and exits the slab.

Snell's Law

Snell's Law is the fundamental relation that describes the refraction of light at an interface between two media. It states that the product of the refractive index and the sine of the angle of incidence in one medium is equal to that in the second medium. This law is essential in calculating the angles of transmission and understanding how light propagates through different layers.

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