Tag: physics

Questions Related to physics

A spherometer has 10 threads per cm and its circular scale has 50 divisions. The least count of the instrument is  

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $0.01 cm$

  2. $0.02 cm$

  3. $0.002 cm$

  4. $0.2 cm$

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Correct Option: C
Explanation:

The least count of the spherometer, $LC=$pitch/ total number of circular divisions $=\dfrac{p}{n}$
Here, pitch $p=1/20=0.1\ cm$ and $n=50$
Thus, $LC=\dfrac{0.1}{50}=0.002\ cm$

If a star is $5.2\times 10^{16}\ m$ away. What is the parallax angle in degrees?

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $1.67 \times 10^{-4}$ degrees

  2. $1.67 \times 10^{-5}$ degrees

  3. $0.67 \times 10^{-4}$ degrees

  4. $2.3 \times 10^{-4}$ degrees

Show answer
Correct Option: A
Explanation:

Given :    $1$ AU $ = 1.5\times 10^11$ m                $d = 5.2\times 10^{15}$ m

Parallax angle:     $\alpha = \dfrac{1 AU}{d} =\dfrac{1.5\times 10^{11}}{5.2\times 10^{16}} = 0.288\times 10^{-5}$  radians
$\implies$   $\alpha = \dfrac{180}{\pi} \times 0.288\times 10^{-5} = 1.67\times 10^{-4}$  degrees

A star is $1.45\ parsec$ light years away. How much parallax would this star show when viewed from two locations of the earth six months apart in its orbit around the sun?

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $2\ Parsec$

  2. $0.725\ Parsec$

  3. $1.45\ Parsec$

  4. $2.9\ Parsec$

Show answer
Correct Option: A
Explanation:

One light year $=$ speed of light $\times$ one year

or $1 ly=3\times 10^8\times (24\times 3600)=94608\times 10^{11} m$
So, $4.29 ly=4.29\times (94608\times 10^{11})=4.058\times 10^{16} m$
As $1 $ parsec $=3.08\times 10^{16} m$
(Parsec is a unit of length used to measure large distances to objects outside our Solar System)
Thus, $4.29 ly=\dfrac{4.058\times 10^{16}}{3.08\times 10^{16}}=1.32$ parsec
Now angular displacement , $\theta=\dfrac{d}{D}$
where $d=$ diameter of earth's orbit $= 3\times 10^{11} m$ and 
$D=$ distance of star from the earth $=4.058\times 10^{16} m$
So, $\theta=\dfrac{3\times 10^{11}}{4.058\times 10^{16}}=7.39\times 10^{-6}$ rad
As $1 sec=4.85\times 10^{-6} rad$ so, $7.39\times 10^{-6} rad=\dfrac{7.39\times 10^{-6}}{4.85\times 10^{-6}}=1.52 sec$

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 :

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

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

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

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

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

Show answer
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

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

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

Show answer
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:

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

  1. $(D/8)$

  2. $(D/4)$

  3. $(D/2)$

  4. D

Show answer
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 :

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

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

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

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

  4. Infinite

Show answer
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:

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

  1. 0.075$^{\circ}$

  2. 0.085$^{\circ}$

  3. 0.095$^{\circ}$

  4. 0.065$^{\circ}$

Show answer
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 :

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

  1. 0.65$^{\circ}$

  2. 0.84$^{\circ}$

  3. 0.48$^{\circ}$

  4. 1.26$^{\circ}$

Show answer
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

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

  1. The greatest for red light

  2. the least for red light

  3. the least for yellow light

  4. the ate for at colours

Show answer
Correct Option: B
Explanation:

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