(D) From Snell's law,$\mu_1 \sin i = \mu_2 \sin r$,which implies $\frac{\sin r}{\sin i} = \frac{\mu_1}{\mu_2}$.From the given graph,the slope is $\tan

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(D) From Snell's law,$\mu_1 \sin i = \mu_2 \sin r$,which implies $\frac{\sin r}{\sin i} = \frac{\mu_1}{\mu_2}$.From the given graph,the slope is $\tan 30^\circ = \frac{\sin r}{\sin i} = \frac{1}{\sqrt{3}}$.Therefore,$\frac{\mu_1}{\mu_2} = \frac{1}{\sqrt{3}}$,which means $\mu_2 = \sqrt{3} \mu_1$.Since $\mu = \frac{c}{v}$,we have $\frac{\mu_2}{\mu_1} = \frac{v_1}{v_2} = \sqrt{3} \approx 1.73$.Thus,$v_1 = 1.73 v_2$,which confirms statement $(b)$.The critical angle $i_c$ is given by $\sin i_c = \frac{\mu_{rarer}}{\mu_{denser}} = \frac{\mu_1}{\mu_2} = \frac{1}{\sqrt{3}}$,which confirms statement $(c)$.Therefore,both $(b)$ and $(c)$ are correct.

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

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When light is incident on a medium at angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin i$ vs $\sin r$ is as shown in the figure. From this,one can conclude that:

A
Velocity of light in the second medium is $1.73$ times the velocity of light in the first medium.
B
Velocity of light in the first medium is $1.73$ times the velocity in the second medium.
C
The critical angle for the two media is given by $\sin i_c = \frac{1}{\sqrt{3}}$.
D
Both $(b)$ and $(c)$.

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Mix Examples-Ray Optics

An object is placed on the principal axis of a convex lens of focal length $10\,cm$ as shown. $A$ plane mirror is placed on the other side of the lens at a distance of $20\,cm$. The final image produced by the plane mirror is $5\,cm$ behind the mirror. The distance of the object from the lens is $............cm$.

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As shown in the figure, a parallel beam of light is incident on the upper part of a prism of angle $1.8^{\circ}$ and material of refractive index $1.5$. The light emerging from the prism falls on a concave mirror of radius of curvature $40 \,cm$. The distance of the point from the principal axis of the mirror where the light rays are focused after reflection from the mirror is:

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Correct exposure for a photographic print is $10 \, s$ at a distance of $1 \, m$ from a point source of $20 \, cd$. For an equal fogging of the print placed at a distance of $2 \, m$ from a $16 \, cd$ source,the necessary time for exposure is.......$s$.

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If $\hat{n}_1$ is the unit vector along the incident ray,$\hat{n}_2$ is the unit vector along the normal,and $\hat{n}_3$ is the unit vector along the reflected ray,then which of the following must be true?

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$A$ luminous object is placed $20 \, cm$ from the surface of a convex mirror and a plane mirror is adjusted in such a way that the virtual images formed by the two mirrors coincide. If the focal length of the convex mirror is $5 \, cm$,then the distance between the plane mirror and the object will be......$cm$.

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When light is incident on a medium at angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin i$ vs $\sin r$ is as shown in the figure. From this,one can conclude that:

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Correct exposure for a photographic print is $10 \, s$ at a distance of $1 \, m$ from a point source of $20 \, cd$. For an equal fogging of the print placed at a distance of $2 \, m$ from a $16 \, cd$ source,the necessary time for exposure is.......$s$.

If $\hat{n}_1$ is the unit vector along the incident ray,$\hat{n}_2$ is the unit vector along the normal,and $\hat{n}_3$ is the unit vector along the reflected ray,then which of the following must be true?

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