Tag: reflection of light in spherical mirrors

Questions Related to reflection of light in spherical mirrors

Which of the following statements is correct according to New Cartesian Sign Convention?

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 of a concave mirror is positive and that of a convex mirror is negative.

  2. Focal length of a concave mirror is negative and that of a convex mirror is positive.

  3. Image distance is always positive for a concave mirror.

  4. The height of all the real and inverted images is positive.

Show answer
Correct Option: B
Explanation:

The focal length of a concave mirror, with a real focus, is always positive as is measured against the direction of incident light.

The focal length of a convex mirror, with a virtual focus, is always negative as is measured along the direction of the incident light.

A convex lens of focal length 0.12 m produces a virtual n image which is thrice the size of the object. Find the distance between the object and the lens

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

  1. 0.04 m

  2. 0.08 m

  3. 0.12 m

  4. 0.24 m

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Correct Option: B
Explanation:

From lens formula
$\dfrac{{1}{v}-\dfrac{1}u}=\dfrac{1}{f}$
$\dfrac{u}{v}-1=\dfrac{u}{f}$
$\dfrac{u}{v}=\dfrac{u+f}{f}$
$\dfrac{v}{u}=\dfrac{f}{u+f}$
For a convex lens f = 0.12m and m=3 then find u
So ,  $3=\dfrac{0.12}{0.12+u}$
$0.36+3u = 0.12$
$u=-0.08 m$

a) For concave mirror focal length is taken as ........
b) For convex mirror, radius of curvature is taken 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. $a = positive, b = negative$

  2. $a = negative, b = positive$

  3. $a = positive, b = positive$

  4. $a = negative, b = negative$

Show answer
Correct Option: B
Explanation:

According to cartesian system focal length of a concave mirror is negative whereas radius of curvature of convex mirror is positive.

A $2.0 cm$ object is placed $15 cm$ in front of a concave mirror of focal length $10 cm$. What is the size and nature of the image?

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

  1. $4 cm$, real

  2. $4 cm$, virtual

  3. $1.0 cm$, real

  4. None of these

Show answer
Correct Option: A
Explanation:

$\dfrac { 1 }{ v } -\dfrac { 1 }{ 15 } =\dfrac { 1 }{ -10 } $
$\Rightarrow v=-30cm$
$\therefore m=-\dfrac { v }{ u } =-\dfrac { -30 }{ 15 } =2$
So, image size will be $4 cm$ (real)

A $2.0\ cm$ long object is placed perpendicular to the principal axis of a concave mirror. The distance of the object from the mirror is $30\ cm$, and its image is formed $60\ cm$ from the mirror, on the same side of the mirror as the object. Find the height of the image formed :

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

  1. $3\ cm$

  2. $4\ cm$

  3. $5\ cm$

  4. $8\ cm$

Show answer
Correct Option: B
Explanation:

Distance of object from the mirror, $u=-30$ 


Distance of image from the mirror, $v=-60$ , image is real.


Now we know  magnification ratio $m=-\dfrac{v}{u}$

$m=-\dfrac{-60}{-30}$

$m=-2$

Height of object $h=2 cm$

Image height $h _1=m\times h=-2\times 2=-4cm$

Height of image is 4 cm and its inverted .

Magnification m = _____

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

  1. v/u

  2. u/v

  3. $h _0/h _i$

  4. $h _i/h _0$

Show answer
Correct Option: A,D
Explanation:

The magnification equation relates the ratio of the image distance(v) and object distance(u) and also to the ratio of the image height ($h _i$) and object height ($h _o$).

i.e., $m=\dfrac vu=\dfrac {h _i}{h _o}$

In a car a rear view mirror having a radius of curvature 1.50 m forms a virtual image of a bus located 10.0 m from the mirror. The factor by which the mirror magnifies the size of the bus is close to

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

  1. 0.06

  2. 0.07

  3. 0.08

  4. 0.09

Show answer
Correct Option: B
Explanation:

R=1.5, u=$-10$

$\dfrac{2}{R}=\dfrac{1}{v}+\dfrac{1}{u}$
$v=\dfrac{30}{43}$
$m=\dfrac{-v}{u}=.069=.07$

A convex lens is used to form an image of an object on a screen. If the upper half of the lens is blackened so that it becomes opaque, then

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

  1. Only half of the image will be visible

  2. The image position shifts towards the lens

  3. The image position shifts away from the lens

  4. The brightness of the image reduces

Show answer
Correct Option: D
Explanation:

To form a image only two rays are needed .The total amount of light released by the object is not allowed to pass through the lens, intensity of image will decrease

An object is kept on the principal axis of a concave mirror of focal length $10$cm, at a distance of $15$cm from its pole. The image formed by the 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. Virtual and magnified

  2. Virtual and diminished

  3. Real and magnified

  4. Real and diminished

Show answer
Correct Option: C
Explanation:

Focal length of concave mirror  $f = -10 \ cm$
Object distance   $u = -15 \ cm$
Using     $\dfrac{1}{v}+\dfrac{1}{u} = \dfrac{1}{f}$
$\therefore$   $\dfrac{1}{v}+\dfrac{1}{-15} = \dfrac{1}{-10}$
$\implies   \ v = -30 \ cm$
Since $v$ is negative, so image formed is real.
Magnification  $m = \dfrac{-v}{u}$
$\therefore$  $m = -\dfrac{(-30)}{-15} = -2$
Since $m$ is greater than $1$, so magnified image is formed.
Correct answer is option C.

From the understanding of cartesian sign convention for reflection by spherical mirror,  students took part in group discussion for FA - 1 in classroom. Who is wrong in the group discussion?
Alpesh : All the distances are measured from the pole of a mirror parallel to the principal axis.
Beena : The distances measured in the direction of incident ray are taken positive.
Chamak : The height measured upward and perpendicular to principal axis is taken negative.
Daksha : The height measured downward and perpendicular to principal axis is taken as positive.

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

  1. Champak and Daksha

  2. Only Champak

  3. Alpesh and Beena

  4. Only Daksha

Show answer
Correct Option: A
Explanation:

1- It is true that all the distances are measured from the pole of a mirror parallel to the principal axis.So, Alpesh is right.

2-It is also true that the distances measured in the direction of incident ray are taken positive.So, Beena is also right
3-The height measured upward and perpendicular to principal axis is taken positive. So, Chamak is wrong.
4-The height measured downward and perpendicular to principal axis is taken as negative.So, Daksha is also wrong.
So, only Champak and Daksha are wrong.
Therefore, A is correct option.