Tag: reflection of light in spherical mirrors

Questions Related to reflection of light in spherical mirrors

The radius of curvature for a plane mirror is

physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

  1. Positive

  2. Negative

  3. Infinite

  4. None of these

Show answer
Correct Option: C
Explanation:

Plane mirrors are not curved.

The distance at which an object should be placed in front of a convex lens of focal length 10 cm to obtain a real image double the size of object will be:

physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

  1. 30 cm

  2. 15 cm

  3. 5 cm

  4. 10 cm

Show answer
Correct Option: B
Explanation:

Convex lens gives the real and double-sized image when the object is placed exactly between the focus and radius of curvature.
We have, $\displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$m = \displaystyle \frac{v}{u} = 2$ or $v = 2u$


$\therefore \displaystyle \frac{1}{f} = \frac{1}{2u} - \frac{1}{-u} = \frac{1}{2u} + \frac{1}{u} = \frac{3}{2u}$

or $\displaystyle \frac{1}{10} = \frac{3}{2u}$ or $u = 15 cm$

The focal length of a convex mirror is $10cm$. Its radius of curvature will be:

physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

  1. $5cm$

  2. $10cm$

  3. $20cm$

  4. $30cm$

Show answer
Correct Option: C
Explanation:

The relation between focal length and Radius of curvature is,

$R=2f$
Here focal length is 10cm so,
$R=2\times 10 = 20cm$

An object is placed at the centre of curvature of a concave mirror of radius of curvature $20$cm. The nature and position of the image shall be.

physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

  1. Virtual and $15$cm from the mirror

  2. Real and $20$cm from the mirror

  3. Virtual and $20$cm from the mirror

  4. Real and $10$cm from the mirror

Show answer
Correct Option: B
Explanation:

Image of an object placed at center of curvature is inverted, real and of the same size and is formed at the center of curvature. Hence image will be real and at the center of curvature (20 cm from mirror).

Formula of focal length in convex lens is

physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

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

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

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

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

Show answer
Correct Option: B

An object is placed at a distance of $50\ cm$ from a convex mirror. A plane mirror is placed in front of the convex mirror in such a way that it covers half of the convex mirror. If the distance between object and plane mirror is $30\ cm$ then there is no parallax between the images formed by two mirrors, the radius of curvature of convex mirror will be :

physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

  1. $50\ cm$

  2. $25\ cm$

  3. $12.5\ cm$

  4. $100\ cm$

Show answer
Correct Option: A

Magnification produced by a convex mirror is $\frac { 1 }{ 3 }$, then distance of the object from mirror is

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $\frac { f }{ 3 }$

  2. $\frac { 2f }{ 3 }$

  3. $1f$

  4. $2f$

Show answer
Correct Option: D

A convex lens of focal length 30 cm forms an image of height 2 cm for an object situated at infinity. If a concave lens of focal length 20 cm is placed coaxially at a distance of 26 cm in front of convex lens. then size of final image would be:

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $1.25cm$

  2. $2.5 cm$

  3. $2 cm$

  4. $0.75cm$

Show answer
Correct Option: B

The object distance $u$ for a concave mirror:

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. must be positive

  2. must be negative

  3. must not be negative

  4. may be negative

Show answer
Correct Option: D
Explanation:

Positive and negative sign depend on the assumption of sign conversion.
either side we can consider positive or negative.
Hence Option D.

The linear magnification for a mirror is the ratio of the size of the image to the size of the object, and is denoted by m. Then m is equal to (symbols have their usual meanings).

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $\displaystyle \frac { uf }{ u-f } $

  2. $\displaystyle \frac { uf }{ u+f } $

  3. $\displaystyle \frac { f }{ u-f } $

  4. None of these

Show answer
Correct Option: C
Explanation:

we now,$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$
multiplying by u in above eq.
$\dfrac{u}{f}=\dfrac{u}{v}+\dfrac{u}{u}$
$\dfrac{u}{f}=\dfrac{u}{v}+1$
$\dfrac{u}{f}-1=\dfrac{u}{v}$
$\dfrac{u}{v}=\dfrac{u-f}{f}$
$\dfrac{v}{u}=\dfrac{f}{u-f}  ,  As, m=\dfrac{v}{u}$
$m=\dfrac{f}{u-f}$
hence,option C is correct.