(D) From Snell's Law,$\mu_2 \sin i = \mu_1 \sin r$,which gives $\frac{\mu_1}{\mu_2} = k = \frac{\sin i}{\sin r}$.$1$. When $k = 1$,$\mu_1 = \mu_2$,so

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(D) From Snell's Law,$\mu_2 \sin i = \mu_1 \sin r$,which gives $\frac{\mu_1}{\mu_2} = k = \frac{\sin i}{\sin r}$.$1$. When $k = 1$,$\mu_1 = \mu_2$,so $\sin i = \sin r$,which implies $i = r$. Thus,$|r - i| = 0$. From the graph,this occurs at $k_2$,so $k_2 = 1$.$2$. As $k \rightarrow \infty$,$\frac{\mu_1}{\mu_2} \rightarrow \infty$,which implies $\sin r = \frac{\sin i}{k} \rightarrow 0$,so $r \rightarrow 0$. Then $|r - i| = |0 - i| = i = \pi / 3$. From the graph,this value is $\theta_2$,so $\theta_2 = \pi / 3$.$3$. Total Internal Reflection $(TIR)$ occurs when $k Since all statements are correct,the answer is $(D)$.

Class 12 Physics Ray Optics and Optical Instruments Mix Examples-Ray Optics

The figure shows a ray incident at an angle $i = \pi / 3$. The plot shows the variation of $|r - i|$ versus $k = \frac{\mu_1}{\mu_2}$,where $r$ is the angle of refraction. Based on the graph,which of the following statements is correct?

A
The value of $k_2$ is $1$.
B
The value of $\theta_1 = \pi / 6$.
C
The value of $\theta_2 = \pi / 3$.
D
All of the above.

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Ray Optics and Optical Instruments

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Mix Examples-Ray Optics

Two plane mirrors are at an angle such that a ray incident on one mirror undergoes a total deviation of $240^o$ after two reflections. Which of the following statements is correct?

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$A$ ray of light strikes a plane mirror at an angle of incidence $45^o$ as shown in the figure. After reflection,the ray passes through a prism of refractive index $1.5$,whose apex angle is $4^o$. The angle through which the mirror should be rotated if the total deviation of the ray is to be $90^o$ is

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An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. If the distance between the lens and the mirror is $20\,cm$,find the focal length of the convex mirror in $cm$.

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When a pin is moved along the principal axis of a small concave mirror,the image position coincides with the object at a point $0.5\, m$ from the mirror. If the mirror is placed at a depth of $0.2\, m$ in a transparent liquid,the same phenomenon occurs when the pin is placed $0.4\, m$ from the mirror. The refractive index of the liquid is

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The figure shows a ray incident at an angle $i = \pi / 3$. The plot shows the variation of $|r - i|$ versus $k = \frac{\mu_1}{\mu_2}$,where $r$ is the angle of refraction. Based on the graph,which of the following statements is correct?

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Two plane mirrors are at an angle such that a ray incident on one mirror undergoes a total deviation of $240^o$ after two reflections. Which of the following statements is correct?

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