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Multiple choice problems on prism prism ray optics and optical instruments optics physics

A spectrum is obtained by sending a beam of white light through a prism. A second prism exactly similar to the first one is placed in an inverted position with the sides parallel to the first. Now

  1. A new spectrum will be formed on the screen with double the number of colours present in the previous spectrum

  2. New spectrum will be obtained on the screen with only half the number of colours present in the previous spectrum

  3. Previous spectrum will disappear and we will obtain a white light formed by the fusion of the colours

  4. A spectrum with same number of colours present in the previous spectrum will be formed but their wave lengths will be increased twice
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A spectrum is obtained by sending a beam of white light through a prism. A second prism exactly similar to the first one is placed in an inverted position with the sides parallel to the first. Now the previous spectrum will disappear and we will obtain a white light formed by the fusion of the colours.

As white is composed of seven colors. The seven colors together joins to form white light again. 

Multiple choice problems on prism prism ray optics and optical instruments optics physics

A number of thin prism of prism angle $A$ and refractive index $\mu$ are arranged on periphery of circle such that any light ray entering from one prism move along a regular polygon

  1. number of prism used will be $\cfrac { 4\pi }{ (\mu -1)A } $

  2. If $A$ is rational, $\mu$ must be rational

  3. if $A$ is rational, $\mu$ must be irrational

  4. If $A$ is irrational, $\mu$ must be irrational
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Deviation by one prism: $\delta = (\mu-1)A$


$\therefore$ Deviation of $n$ prism: $\delta' = n\delta = n(\mu-1)A$       

Deviation of light moving along a regular polygon, $\delta' = 2\pi$

$\therefore$   $n(\mu-1)A = 2\pi$          

$\implies n = \dfrac{2\pi}{(\mu -1)A}$

Thus if $A$ is rational, then $\mu$ must be irrational.

Multiple choice problems on prism prism ray optics and optical instruments optics physics

A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu $ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is :

  1. $sin^{-1}\left ( \dfrac{1}{\mu } \right )$

  2. $tan^{-1}\left ( \dfrac{1}{\mu } \right )$

  3. $sin^{-1}\left ( \dfrac{\mu -1}{\mu } \right )$

  4. $cos^{-1}\left ( \dfrac{1}{\mu } \right )$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
If  $\alpha$  is maximum value of base angle for which light is totally reflected from the hypotenuse and  $\theta$  is the minimum value of angle of incidence at hypotenuse for total internal reflection.
Then ,
$ \theta =sin^{-1}\left (  \dfrac{1}{\mu}\right )$

$\alpha +\theta =90^o$

$\Rightarrow \alpha = 90^o-sin^{-1}\left ( 1/\mu \right )=cos^{-1}\left ( 1/\mu \right )$
Multiple choice problems on prism prism ray optics and optical instruments optics physics

A thin prism of angle $15^{o}$ made of glass of refractive index $\mu _{1} = 1.5$ is combined with another prism of glass of refractive index $\mu _{2} = 1.75$. The combination of the prism produced dispersion without deviation. The angle of the second prism should be :

  1. $5^{o}$

  2. $7^{o}$

  3. $10^{o}$

  4. $12^{o}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For without deviation 

$\frac{A}{A'}=-\frac{\mu ' -1}{\mu -1}$

$\frac{15^{o}}{A'}=-\frac{1.75-1}{1.50-1}$

$\frac{15^{o}}{A'}=-\frac{0.75}{0.50}$

$A'=-10^{o}$

Multiple choice problems on prism prism ray optics and optical instruments optics physics

A glass prism has a right-triangular cross-section ABC, with $\angle$A$=90^o$. A ray of light parallel to the hypotenuse BC and incident on the side AB emerges grazing the side AC. Another ray, again parallel to the hypotenuse BC, incident on the side AC suffers total internal reflection at the side AB. Find the range of  the refractive index $\mu$ of the material of the prism?

  1. $\sqrt{\dfrac{3}{2}} < \mu < \sqrt 2$

  2. $\mu > \sqrt 3$

  3. $\mu < \sqrt{\dfrac{3}{2}}$

  4. $\sqrt 2 < \mu < \sqrt 3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The conditions provided for grazing emergence and total internal reflection define the boundaries for the refractive index mu based on the geometry of the right-angled prism.

Multiple choice problems on prism prism ray optics and optical instruments optics physics

A thin prism $P _1$ with angle $6^o$ and made from glass of refractive index 1.54 is combined with another thin prism $P _2$ of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P _2$ will be.

  1. $4^o 30'$

  2. $8.5^o$

  3. $6.5^o$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that for small angle of prism, deviation ,$\delta=A(\mu-1)$

where $A$=angle of prism

Here, net deviaton$A _1(\mu _1-1)-A _2(\mu _2-1)=0$

$\implies A _2=\dfrac{A _1(\mu _1-1)}{\mu _2-1}$

$\implies A _2=\dfrac{6\times 0.54}{0.72}=4.5^{o}$

$\implies A _2=4^{o}30'$

Answer-(A)

Multiple choice problems on prism prism ray optics and optical instruments optics physics

The refracting angle of a prism $60^{\mathrm{o}}$.The refractive index of the material of the prism is $\sqrt{\dfrac{7}{3}}$. The limiting angle of incidence of a ray that will be transmitted through the prism in this case will be :

  1. $30^{0}$

  2. $45^{\mathrm{o}}$

  3. $40^{\mathrm{o}}$

  4. $50^{\mathrm{o}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The limiting angle of incidence is determined by the condition that the ray must be able to pass through the prism without undergoing total internal reflection at the second face.