Tag: sign convention for the measurement of distances

Questions Related to sign convention for the measurement of distances

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. $2f$

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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. $0.75cm$

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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

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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.

The sum of the reciprocals of object distance and image distance is equal to the __________ of a 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. focal length

  2. reciprocal of the focal length

  3. radius of curvature

  4. reciprocal of the radius of curvature

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Correct Option: B
Explanation:

The sum of the reciprocals of object distance and image distance is equal to the reciprocal of the focal length of a mirror.

The relation between $u,\,v\;and\;f$ for a mirror is given by

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

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

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

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

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

Show answer
Correct Option: C
Explanation:

The relation between $u,\,v\;and\;f$ for a mirror is given by $f=\displaystyle\frac{u\times v}{u+v}$

Choose the correct relation between $u,\,v\;and\;r$ for a spherical mirror, where $r$ is radius of curvature.

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

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

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

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

  4. $r=\displaystyle\frac{2uv}{u-v}$

Show answer
Correct Option: A
Explanation:

The relation between $u,\,v\;and\;f$ for a mirror is given by $f=\displaystyle\frac{u\times v}{u+v}$

so $r=\displaystyle\frac{2u\times v}{u+v}$

The unit of magnification 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. $m$

  2. $m^2$

  3. $m^{-1}$

  4. it has no units

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Correct Option: D
Explanation:

Magnification is a ratio of lengths, hence it has no units

The ratio of the size of the image to the size of the object is known as :

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

  1. the focal plane

  2. the transformation ratio

  3. the efficiency

  4. the magnification ratio

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Correct Option: D
Explanation:

magnification ratio is given as:

 size or height of image/ size or height of object
substituted with proper sign convention.

An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. Determine the ratio of the size of the image and the size of object

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

  1. 2:1

  2. 1:2

  3. 1:1

  4. 4:1

Show answer
Correct Option: C
Explanation:

Since focal length of concave mirror given is 20cm l. Object is at 40cm distance which means it is at centre of curvature. hence, image will be formed of same size and at centre focus only but real and inverted.