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Perceive colours - class-XI

Description: perceive colours
Number of Questions: 21
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Tags: lenses physics option c: imaging
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The angles of minimum deviations are 53$^{\circ}$ and 51$^{\circ}$ for blue and red colors respectively produced in an equilateral glass prism. The dispersive power is :

  1. $\dfrac{2}{51}$

  2. $\dfrac{1}{26}$

  3. $\dfrac{1}{52}$

  4. $\dfrac{1}{51}$


Correct Option: B
Explanation:

As $\delta _{Y}=\dfrac{\delta _{B}+\delta _{R}}{2}$


So $\delta _{Y}=\dfrac{53^{\circ }+51^{\circ }}{2}$ =52$^{\circ }$

$\therefore dispersive\ power\ =\dfrac{\delta _{B}-\delta _{R}}{\delta _{Y}}$

                                    $=\dfrac{53-51}{52}$

                                    $=\dfrac{2}{52}$

                                    $=\dfrac{1}{26}$

If the refractive indices of crown glass for red, yellow and violet colours are respectively ${ \mu  } _{ r },{ \mu  } _{ y },{ \mu  } _{ v }$, then the dispersive power of this glass would be

  1. $\cfrac { { \mu } _{ v }-{ \mu } _{ r } }{ { \mu } _{ y }-1 } $

  2. $\cfrac { { \mu } _{ v }-{ \mu } _{ y } }{ { \mu } _{ r }-1 } $

  3. $\cfrac { { \mu } _{ v }-{ \mu } _{ y } }{ { \mu } _{ y }-{ \mu } _{ r } } $

  4. $\cfrac { { \mu } _{ v }-{ \mu } _{ r } }{ { \mu } _{ y } } -1$


Correct Option: A
Explanation:

Dispersive power of a glass is given by ratio of difference of reflective index of two extreme wavelength to the difference of intermediate wavelength to unity i.e.


$ { Dispersive\quad Power\quad =\quad \dfrac { { \mu  } _{ v }-{ \mu  } _{ r } }{ { \mu  } _{ y }-1 }  } $

The dispersion of a medium for wavelength $\lambda$ is D. Then the dispersion for the wavelength $2\lambda$ will be:

  1. $(D/8)$

  2. $(D/4)$

  3. $(D/2)$

  4. D


Correct Option: A
Explanation:

As we know, Cauchy's Dispersion formula is :
$ \mu $= $A + \dfrac{B}{ \lambda^{^{2}}} $
And dispersion
D= - $ \dfrac {d\mu}{d\lambda}$
Therefore, from the above 2 equations:
D = $ -(-2\lambda ^{3})B $= $ \dfrac {2B}{\lambda^{3}}$
This implies that
D $ \alpha \dfrac{1}{\lambda^{3}}$
Hence,
$ \dfrac {{D}'}{D}$ = $( \dfrac{\lambda}{{\lambda}' })^{3}$
As $ {\lambda}' = 2\lambda$
Therefore,
$ {D}' =D/8$

In a prism, the refractive indices of different colours are
$\mu _{V} =$ 1.6;
$\mu _{R} =$ 1.52;
$\mu _{Y} =$ 1.56.
The dispersive power of the prism is :

  1. $\dfrac{1}{56}$

  2. $\dfrac{1}{8}$

  3. $\dfrac{1}{7}$

  4. Infinite


Correct Option: C
Explanation:

Dispersive power of prism= $w=\dfrac{\mu _{V}-\mu _{R}}{\mu _{Y}-1}$


$w=\dfrac{1.6-1.52}{1.56-1}$

$w=\dfrac{1}{7}$

A flint glass prism is of refracting angle 5$^{\circ}$. Its refractive index for C line is 1.790 and for F line is 1.805. The angular dispersion of C and F lines is:

  1. 0.075$^{\circ}$

  2. 0.085$^{\circ}$

  3. 0.095$^{\circ}$

  4. 0.065$^{\circ}$


Correct Option: A
Explanation:

Deviation for C line $= \text{(Refractive index for C line -1) x Refracting angle}$

                                 $= (1.79-1) \times 5$
                                 $=3.95^o$

Deviation for F line $= \text{(Refractive index for F line -1) x Refracting angle}$

                                 $= (1.805-1) \times 5$      
                                 $= 4.025^o$

So the angular dispersion of C and F line is the deviation difference between F and C line.
Angular dispersion $= 4.025 -3.95 = 0.075^o$

Dispersive power of the material of a prism is 0.0221. If the deviation produced by it for yellow colour is 38$^{\circ}$, then the angular dispersion between red and violet colours is :

  1. 0.65$^{\circ}$

  2. 0.84$^{\circ}$

  3. 0.48$^{\circ}$

  4. 1.26$^{\circ}$


Correct Option: B
Explanation:

As Dispersive power $ = \dfrac{Angular  \  dispersion}{mean  \ deviation}$


We take the deviation for yellow color as the mean deviation

$\Longrightarrow$  $\omega=\dfrac{\delta _{V}-\delta _{R}}{\delta _{Y}}$


$\Longrightarrow$  $0.0221=\dfrac{\delta _{V}-\delta _{R}}{38^{\circ }}$

$\Longrightarrow$  $\delta _{\nu}-\delta _{R}=0.84^{\circ }$

The dispersive power of a medium is

  1. The greatest for red light

  2. the least for red light

  3. the least for yellow light

  4. the ate for at colours


Correct Option: B
Explanation:

We know $ P \propto\frac {1}{f}$ focal length is maximum for red light.

The difference between angle of minimum deviation for violet and red rays in the spectrum of white light from a prism is $2^0$. If the angle of minimum deviation of the mean ray is $48^0$, the dispersive power of the material of the prism is

  1. $24^0$

  2. $48^0$

  3. 0.0416

  4. 0.0832


Correct Option: D

The focal length of a thin convex lens for red and blue rays are $100\ cm$ and $96.8\ cm$ respectively. The dispersive power of the material of the lens is

  1. 0.0325

  2. 0.825

  3. 0.968

  4. 0.98


Correct Option: A

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

  1. increases

  2. decreases

  3. does not change

  4. may increase or decrease depending on whether the angle of the prism is less than or greater than $60^o$


Correct Option: A
Explanation:

Dispersive power of a prism $=\dfrac{\mu _{v}-\mu _{r}}{\mu-1}$


Here the refractive indices are with respect to the medium in which prism is kept.

Hence when in water, dispersive power $=\dfrac{\dfrac{\mu _{v}}{\mu _{water}}-\dfrac{\mu _{r}}{\mu _{water}}}{\dfrac{\mu}{\mu _{water}}-1}$
$=\dfrac{\mu _{v}-\mu _{r}}{\mu-\mu _{water}}$

Hence dispersive power increases when prism is dipped in water.

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

  1. 4 : 3

  2. 3 : 4

  3. 1 : 1

  4. 9 : 16


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 :

  1. $0.3$

  2. $3.3$

  3. $1.33$

  4. $.03$


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 :

  1. 0.0276

  2. 0.276

  3. 2.76

  4. 0.106


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                  

  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


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

  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


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

  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 }$


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 :

  1. 5:4

  2. 4:5

  3. 25:28

  4. 5:28


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

  1. $11 : 9$

  2. $6 : 5$

  3. $9 : 11$

  4. $5 : 6$


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.

  1. Polarised

  2. Of longer wavelength largest

  3. Of shorter wavelength

  4. Of high intensity


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 $\mu _r=1.5145$.

  1. 0.0012

  2. 0.2333

  3. 0.1639

  4. 0.9


Correct Option: C
Explanation:

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

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

If the refractive indices of a prism for red, yellow and violet colours be 1.61, 1.63 and 1.65 respectively, then the dispersive power of the prism will be:

  1. $\dfrac { 1.65-1.62 }{ 1.61-1 }$

  2. $\dfrac { 1.62-1.61 }{ 1.65-1 }$

  3. $\dfrac { 1.65-1.61 }{ 1.63-1 }$

  4. $\dfrac { 1.65-1.63 }{ 1.61-1 }$


Correct Option: C
Explanation:

Dispersive power of the prism=$\dfrac{\mu _v-\mu _r}{\mu _y-1}=\dfrac{1.65-1.61}{1.63-1}$

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