Tag: reflection of light at curved surfaces

Questions Related to reflection of light at curved surfaces

What is the formula for spherical mirrors for object distance p and image distance q ?

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $\dfrac{1}{p}+q=\dfrac{1}{f}$

  2. $\dfrac{1}{p}+\dfrac{1}{q}=\dfrac{1}{f}$

  3. $\dfrac{1}{p}+\dfrac{1}{q}=f$

  4. $p+\dfrac{1}{q}=\dfrac{1}{f}$

Show answer
Correct Option: B
Explanation:
Mirror formula is given as: 
$ \dfrac{2}{R} = \dfrac{1}{v} + \dfrac{1}{u} $

where, $ R $ is the radius of curvature of the spherical mirror
$u $ is the object distance from the pole
$ v $ is the image distance from the pole

We know,
$ f = \dfrac{R}{2} $

$ \Rightarrow \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} $

$ \therefore $ For object distance $ p $ and image distance $ q $, mirror formula becomes
$ \dfrac{1}{f} = \dfrac{1}{p} + \dfrac{1}{q} $

Hence, the correct answer is OPTION B.

The relation between u, v and r is:

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $r=\dfrac {2uv}{u+v}$

  2. $r=\dfrac {2}{u+v}$

  3. $r=\dfrac {2(u+v)}{(uv)}$

  4. None of these

Show answer
Correct Option: A
Explanation:

We know,
$ 1/f = 1/u +1/v$
Or $2/r = 1/u +1/v$
Since radius of curvature is double the focal length. This leads to option A.

A plane mirror produces an image that is

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. Real, inverted and larger than the object.

  2. Real, upright and same size as the object.

  3. Real upright and smaller than the object.

  4. Virtual, upright and the same size of the object.

Show answer
Correct Option: D

A point object is placed at a distance $10cm$ and its real image is formed at a distance of $20cm$ from concave mirror. If the object is moved by $0.1cm$ towards the mirror, the image will shift by about

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $0.4cm$ away from the mirror

  2. $0.4cm$ towards the mirror

  3. $0.8cm$ away from the mirror

  4. $0.8cm$ towards the mirror

Show answer
Correct Option: A
Explanation:

$We\quad know\quad \dfrac { 1 }{ f } =\dfrac { 1 }{ u } +\dfrac { 1 }{ v } ;\quad \ where\quad f=focal\quad length=?\ u=\quad initial\quad distance=20\quad cm\ v=\quad final\quad distance=10cm\ \dfrac { 1 }{ f } =\dfrac { 1 }{ -20 } +\dfrac { 1 }{ (-10) } \ f=\dfrac { 20 }{ 3 } \quad cm\ Now\quad object\quad moved\quad towards\quad the\quad mirror=0.1\quad cm,so\quad the\quad new\quad value\quad of\quad u=9.9\quad cm\ Again\quad \quad \quad \ \dfrac { 1 }{ f } =\dfrac { 1 }{ { u } _{ 1 } } +\dfrac { 1 }{ { v } _{ 1 } } \ \dfrac { 1 }{ f } -\dfrac { 1 }{ { u } _{ 1 } } =\dfrac { 1 }{ { v } _{ 1 } } \ \dfrac { 1 }{ { v } _{ 1 } } =\quad \dfrac { 3 }{ 20 } -\dfrac { 1 }{ (-9.9) } \ { v } _{ 1 }=20.4\quad cm\ The\quad change\quad in\quad final\quad distance\quad =20.4cm\quad -20\quad cm=0.4\quad cm\ \ v=\dfrac { 9\times 1600 }{ 3600 } =\quad 4cm/s$

A plane mirror produces a magnification of

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $-1$

  2. $+1$

  3. Zero

  4. infinity

Show answer
Correct Option: B
Explanation:

The magnification produced by a plane mirror is $+1$ implies that the image formed by a plane mirror is virtual$,$

erect and of the same size$,$ as that of object$.$
Hence,
option $(B)$ is correct answer.

If two mirrors are inclined at some angle $\theta$. An object is placed between the mirrors and there are 5 images formed for an object, then $\theta$ is may be

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $45^o$

  2. $53^o$

  3. $63^o$

  4. $75^o$

Show answer
Correct Option: C
Explanation:

The number of images formed by two mirrors at an angle $\theta $ is

$\begin{array}{l} n=\dfrac { { 360 } }{ \theta  } -1 \ \because n=5\, \, \left( { given } \right)  \ \therefore 5=\dfrac { { 360 } }{ \theta  } -1 \ \therefore \theta =\dfrac { { 360 } }{ 6 } ={ 60^{ 0 } } \end{array}$
Hence, the angle may be $63^0$.

The relation between $u, v$ ( u is the object distance and v is the image distance )  and f for mirror is given by:

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $\displaystyle f=\frac{uv}{u-v}$

  2. $\displaystyle f=\frac{2u\times v}{u+v}$

  3. $\displaystyle f=\frac{u\times v}{u+v}$

  4. none of these

Show answer
Correct Option: C
Explanation:

$\dfrac{1}{u} +\dfrac{1}{v} = \dfrac{1}{f} $

or $\dfrac{u+v}{uv} = \dfrac{1}{f}$
or $f=\dfrac{uv}{u+v}$

A point source of light is kept in front of a convex mirror of radius of curvature $40 cm$. The image is formed at $10 cm$ behind the mirror. Calculate the object distance

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. 30

  2. 20

  3. 50

  4. 40

Show answer
Correct Option: B
Explanation:

Given: For a convex mirror, $R = -40 cm$.
$v = -10 cm$ (image is virtual).
From mirror formula, we have

$\displaystyle \frac {2}{R}=\frac {1}{u}+\frac {1}{v}$

$\displaystyle \frac {1}{u}=\frac {2}{R}-\frac {1}
{v}=\frac {2v-R}{vR}$

$\displaystyle u=\frac {vR}{2v-R}=\frac {(-10cm) \times (-40cm)}{2 \times (-10cm) - (-40cm)}$

$=+20cm$
Thus, object is placed $20 cm$ in front of the mirror.

Mirror formula is valid for:

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. Convex mirror

  2. Concave mirror

  3. Both A and B

  4. For lenses and mirrors

Show answer
Correct Option: C
Explanation:
Mirror formula is:
$\dfrac {1}{v} + \dfrac {1}{u} = \dfrac {1}{f}$
That is; $\dfrac {1}{\text {Object Distance}} + \dfrac {1}{\text {Image Distance}} = \dfrac {1}{\text {Focal length of the mirror}}$
This relationship is applicable for both concave and convex mirrors.

Mirror formula can also be written as:

physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

  1. $\dfrac {1}{2v} + \dfrac {1}{2u} = \dfrac {1}{2f}$

  2. $\dfrac {1}{v} + \dfrac {1}{u} = \dfrac {2}{R}$

  3. $\dfrac {1}{v} + \dfrac {2}{u} = \dfrac {1}{f}$

  4. $\dfrac {1}{2v} + \dfrac {4}{u} = \dfrac {3}{R}$

Show answer
Correct Option: B
Explanation:

Focal length, $f = \dfrac {R}{2}$, where $R$ = radius of curvature

So, $\dfrac {1}{v} + \dfrac {1}{u} = \dfrac {1}{f}$ can be written as
$\Rightarrow \dfrac {1}{v} + \dfrac {1}{u} = \dfrac {2}{R}$