Tag: optics

Questions Related to optics

The refractive index of a prism is 2. The prism can have a maximum refracting angle of

problems on prism prism ray optics and optical instruments optics physics

  1. $90^o$

  2. $60^o$

  3. $45^o$

  4. $30^o$

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Correct Option: B
Explanation:

Critical angle of the prism such that it does not refract back into the prism from the emerging side $=\theta _c=sin^{-1}(\dfrac{1}{\mu})=sin^{-1}\dfrac{1}{2}=30^{\circ}$


The angles made by the ray inside the prism cannot be greater than $30^{\circ}$.


$A=r _1+r _2$

If $A>60^{\circ}$, the ray does not emerge from the prism. So maximum refracting angle can be $60^{\circ}$.

A ray of monochromatic light is incident on the refracting face of a prism (angle $75^o$). It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the prism is $\sqrt 2$, then the angle of incidence on the first face of the prism is :

problems on prism prism ray optics and optical instruments optics physics

  1. $15^o$

  2. $30^o$

  3. $45^o$

  4. $60^o$

Show answer
Correct Option: C
Explanation:
As the ray on the other face is incident on critical angle $r^{'}=sin^{-1}\dfrac{1}{\mu}=sin^{-1}\dfrac{1}{\sqrt{2}}=45^o$

So the refracting angle on first surface $r=A-r^{'}=75^o-45^o=30^o$

Applying snell's law for first surface,

$\mu _{1}sin\alpha _{1}=\mu _{2}sin\alpha _{2}$ 

$1\times sin i=\sqrt{2}sin30^o$

$i=45^o$, hence option $C$ is correct. 

A beam of light consisting of red, green, and blue colors is incident on a right-angled prism. The refractive indices of the material of the prism for the above red, green, and blue wavelengths are 1.39, 1.44, and 1.47, respectively. The prism will

problems on prism prism ray optics and optical instruments optics physics

  1. separate part of the red color from the green and blue color

  2. separate part of the blue color from the red and green color

  3. separate all the three colors from one another

  4. not separate even partially any color from the other two colors

Show answer
Correct Option: A
Explanation:

The prism will separate part of the red color from the green and blue color as the refractive index are different hence they undergo different deviations
hence correct option is $A$.

A thin prism of angle $7^o$ made of glass of refractive index $1.5$ is combined with another prism made of glass of $\mu =1.75$ to produce dispersion without deviation. The angle of second prism is :

problems on prism prism ray optics and optical instruments optics physics

  1. $7^o$

  2. $4.67^o$

  3. $9^o$

  4. $5^o$

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Correct Option: B

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

problems on prism prism ray optics and optical instruments optics physics

  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

Show answer
Correct Option: C
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. 

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

problems on prism prism ray optics and optical instruments optics physics

  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

Show answer
Correct Option: C
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.

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 :

problems on prism prism ray optics and optical instruments optics physics

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

Show answer
Correct Option: D
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 )$

$\alpha +\theta =90^o$

$\Rightarrow \alpha = 90^o-sin^{-1}\left ( 1/\mu \right )=cos^{-1}\left ( 1/\mu \right )$

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 :

problems on prism prism ray optics and optical instruments optics physics

  1. $5^{o}$

  2. $7^{o}$

  3. $10^{o}$

  4. $12^{o}$

Show answer
Correct Option: C
Explanation:

For without deviation 

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

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

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

$A'=-10^{o}$

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?

problems on prism prism ray optics and optical instruments optics physics

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

  2. $\mu > \sqrt 3$

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

  4. $\sqrt 2 < \mu < \sqrt 3$

Show answer
Correct Option: A

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.

problems on prism prism ray optics and optical instruments optics physics

  1. $4^o 30'$

  2. $8.5^o$

  3. $6.5^o$

  4. None of these

Show answer
Correct Option: A
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)