(A) For the light ray to retrace its path,it must strike the silvered surface normally (at an angle of $90^{\circ}$).In the triangle formed inside the

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(A) For the light ray to retrace its path,it must strike the silvered surface normally (at an angle of $90^{\circ}$).In the triangle formed inside the prism,the angle at the silvered surface is $90^{\circ}$,and the angle at the apex is $A$. Thus,the angle of refraction $r$ at the first surface must be $r = 90^{\circ} - A$.According to Snell's Law at the first surface: $\mu = \frac{\sin i}{\sin r}$.Given $i = 2A$ and $r = 90^{\circ} - A$,we have:$\mu = \frac{\sin(2A)}{\sin(90^{\circ} - A)}$$\mu = \frac{2 \sin A \cos A}{\cos A}$$\mu = 2 \sin A$.

Class 12 Physics Ray Optics and Optical Instruments Refraction Through Prism

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The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:

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A
$2 \sin A$
B
$2 \cos A$
C
$\frac{1}{2} \cos A$
D
$\tan A$

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Ray Optics and Optical Instruments

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Refraction Through Prism

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$A$ ray of light passes through an equilateral prism such that the angle of incidence $(i)$ is equal to the angle of emergence $(e)$. The angle of emergence is equal to $\left(\frac{3}{4}\right)$ of the angle of the prism. The angle of deviation is: (in $^{\circ}$)

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$A$ certain prism is found to produce a minimum deviation of $38^\circ$. It produces a deviation of $44^\circ$ when the angle of incidence is either $42^\circ$ or $62^\circ$. What is the angle of incidence when it is undergoing minimum deviation (in $^\circ$)?

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$A$ prism has a refracting angle of $30^\circ$ and a refractive index of $\sqrt{2}$. One of its faces is silvered. At what angle of incidence $i$ should a ray be incident on the other face so that it retraces its path after reflection from the silvered face?

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Three prisms of crown glass,each having a prism angle of $9^o$,and two prisms of flint glass are used to make a direct vision spectroscope. What will be the angle of the flint glass prisms in degrees if the refractive index $\mu$ for flint glass is $1.60$ and $\mu$ for crown glass is $1.53$ (in $^o$)?

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The angle of prism is $5^o$ and its refractive indices for red and violet colours are $1.5$ and $1.6$ respectively. The angular dispersion produced by the prism is.....$^o$

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The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:

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$A$ ray of light passes through an equilateral prism such that the angle of incidence $(i)$ is equal to the angle of emergence $(e)$. The angle of emergence is equal to $\left(\frac{3}{4}\right)$ of the angle of the prism. The angle of deviation is: (in $^{\circ}$)

$A$ certain prism is found to produce a minimum deviation of $38^\circ$. It produces a deviation of $44^\circ$ when the angle of incidence is either $42^\circ$ or $62^\circ$. What is the angle of incidence when it is undergoing minimum deviation (in $^\circ$)?

$A$ prism has a refracting angle of $30^\circ$ and a refractive index of $\sqrt{2}$. One of its faces is silvered. At what angle of incidence $i$ should a ray be incident on the other face so that it retraces its path after reflection from the silvered face?

The angle of prism is $5^o$ and its refractive indices for red and violet colours are $1.5$ and $1.6$ respectively. The angular dispersion produced by the prism is.....$^o$

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