Tag: resolution of optical instruments

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Questions Related to resolution of optical instruments

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

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. $\dfrac{1}{51}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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


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

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

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

                                    $=\dfrac{2}{52}$

                                    $=\dfrac{1}{26}$

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

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. $\cfrac { { \mu } _{ v }-{ \mu } _{ r } }{ { \mu } _{ y } } -1$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 }  } $

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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$

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

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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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


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

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

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

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$^{\circ}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $= 4.025 -3.95 = 0.075^o$

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

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$^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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


We take the deviation for yellow color as the mean deviation

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


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

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

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Dispersive power (omega) for a thin lens is (f_r - f_b) / f_mean. f_mean = (100 + 96.8) / 2 = 98.4. Omega = (100 - 96.8) / 98.4 = 3.2 / 98.4 = 0.0325.

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

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 $60^o$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.