Tag: resolution of optical instruments

Questions Related to resolution of optical instruments

Two thin prisms of flint glass, with refracting angles of $6^o$ and $8^o$ respectively, possess disperse powers in the ratio 

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. 4 : 3

  2. 3 : 4

  3. 1 : 1

  4. 9 : 16

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Correct Option: C
Explanation:

Dispersive power = $\dfrac{\mu _v-\mu _r}{\mu-1}$ 

Since, it does not depend on angle of prism, dispersive power f both prism will be same.
Therefore, C is correct option.

Refractive index of glass for red and violet colours are $1.64$ and $1.66$ respectively. Dispersive power of the prism is :

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. $0.3$

  2. $3.3$

  3. $1.33$

  4. $.03$

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Correct Option: D

The refractive index of flint glass for blue line is 1.6333 and red line is 1.6161, then dispersive power of the glass is :

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. 0.0276

  2. 0.276

  3. 2.76

  4. 0.106

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Correct Option: A
Explanation:

Given :     $n _b = 1.6333$             $n _r = 1.6161$

Refractive index for yellow light    $n _y = \dfrac{n _b+n _y}{2}$
$\therefore \ n _y = \dfrac{1.6333+1.6161}{2} = 1.6247$
Dispersive power     $w = \dfrac{n _b-n _r}{n _y - 1} = \dfrac{1.6333-1.6161}{1.6247-1} = 0.0276$

Using the following data,choose the correct option:
                     C        D        F      
 Crown   1.5145   1.5170  1.5230   
FLINT    1.6444    1.6520  1.6637                  

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. The dispersive power for crown glass is 0.1644

  2. The dispersive power for flint glass is 0.029601

  3. The dispersive power for crown is 0.01644

  4. The dispersive power for flint glass is 1.29601

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Correct Option: B,C

If D is the deviation of a normally falling light beam on a thin prism of angle a and $\delta$ is the dispersive power of the same prism then

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. D is independent of A

  2. D is independent of refractive Index

  3. $\delta$ is independent of refractive index

  4. $\delta$ is independent of A

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Correct Option: D
Explanation:

Using relation $ D=\left( { \mu  } _{ v }-{ \mu  } _{ r } \right) A$


and $ \delta =\dfrac { { \mu  } _{ v }-{ \mu  } _{ r } }{ { \mu  } _{ y }-1 } $ we get,

$ \delta$ is independent of $A$

If a glass prism is dipped in water, its dispersive power

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. increases

  2. decreases

  3. does not change

  4. may increase or decreases depending on whether the angle of the prism is less than or greater than $ { 60 }^{ \circ }$

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Correct Option: B
Explanation:

Glass prism works on the principle that lights with different colours travels with different speed in solid and liquid medium. So when a glass prism is dipped in water the light that reaches it is already some what dispersed by water, and the prism does still more. Hence its dispersive power decreases.

A thin prism deviates blue and red rays through 10$^{\circ}$ and 6$^{\circ}$respectively. Another prism deviates same colours through 8$^{\circ}$ and 4.5$^{\circ}$ respectively.The ratio of dispersive powers of the prisms is :

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. 5:4

  2. 4:5

  3. 25:28

  4. 5:28

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Correct Option: C
Explanation:

For a thin prism,

Dispersive power, $w = (\delta _{v}-\delta _{r}) / \delta _{y}$

Also, $\delta _{y} = (\delta _{v}+\delta _{r})/2$

Ratio of dispersive power,
$w _{1} : w _{2} = [(10-6) * 2 / (10+6)] : [(8-4.5)*2)/ (8+4.5)]$

=> $w _{1} : w _{2} = 25:28$

A prism of a certain angle deviates the red and blue rays by $8$ and $12$ respectively. Another prism of the same angle deviates the red and blue rays by $10$ and $14$ respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. $11 : 9$

  2. $6 : 5$

  3. $9 : 11$

  4. $5 : 6$

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Correct Option: B
Explanation:
Dispersive power $= \cfrac{\mu _v - \mu _r}{\mu _y -1} = \cfrac{\delta _v + \delta _r}{\delta _y}$

$\delta _y = \cfrac{\delta _v + \delta _r}{2}$

The ratio of dispersive power is;
$\cfrac{12-8}{\cfrac{12+8}{2}}$= $\cfrac{\cfrac{4}{10}}{\cfrac{4}{12}}$ =$ \cfrac{12}{10} $= $ 6 : 5 $

When a beam of light is used to determine the position of an object, the maximum accuracy is achieved if the light is.

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. Polarised

  2. Of longer wavelength largest

  3. Of shorter wavelength

  4. Of high intensity

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Correct Option: C
Explanation:

The resolving power of an instrument depends upon the wave length of light used. The lower the wavelength of light higher is the accuracy in vision.
$\left(Resolving\, power \,\alpha \frac{1}{\lambda}\right)$

Calculate the dispersive power for glass from the given data $\mu _v=1.523$, and $\mu _r=1.5145$.

perceive colours resolution of optical instruments lenses option c: imaging physics

  1. 0.0012

  2. 0.2333

  3. 0.1639

  4. 0.9

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Correct Option: C
Explanation:

Mean refractive index   $\mu = \dfrac{\mu _v+\mu _r}{2} = \dfrac{1.523+1.5145}{2} = 1.5192$

Dispersive power   $w = \dfrac{\mu _v - \mu _r}{\mu -1}$
$\implies \ w = \dfrac{1.523 - 1.5145}{1.5192 -1} = 0.01637$