Physics

Ray Optics and Mirrors

141 Questions

Ray optics covers the principles of light reflection and refraction through mirrors and lenses. The questions focus on focal length, magnification, and image formation. This physics topic is highly relevant for exams requiring science aptitude.

Concave mirror imagesConvex lens formulasFocal length calculationsMagnification ratiosImage distance

Ray Optics and Mirrors Questions

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

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

  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. $p+\dfrac{1}{q}=\dfrac{1}{f}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
Multiple choice physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

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

  1. 30

  2. 20

  3. 50

  4. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice conditions for a light ray to pass undeviated refraction of light at plane surfaces physics

A mark is made on the surface of a glass sphere of diameter 10 cm and refractive index 1.5 . it its viewed through the glass from a potion directly opposite . the distance of the image of the mark from the centre of the sphere will be 

  1. 20 cm

  2. 17.5 cm

  3. 15 cm

  4. 22.5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the refraction formula at a spherical surface: (mu2 / v) - (mu1 / u) = (mu2 - mu1) / R. Here, the object is on the surface, so u = -10 cm (diameter). mu1 = 1.5, mu2 = 1, R = -5 cm. (1 / v) - (1.5 / -10) = (1 - 1.5) / -5 => 1/v + 0.15 = 0.1 => 1/v = -0.05 => v = -20 cm. The image is 20 cm from the pole, which is 20 cm from the center.

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

The focal length of a spherical mirror is half of the radius of curvature

  1. For all rays

  2. Only for paraxial rays near the principal axis

  3. For those rays which are far from the principal axis

  4. For those rays which subtend extremely large angles with the axis
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The rays that are near the principal axis (paraxial rays) and parallel to it converge to a single point on the axis after emerging from the spherical mirror. This point is called the focal point F of the lens.
And this is half of the radius of the curvature in spherical mirror.
Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

Focal length of a spherical mirror is $200 cm$. What will be its radius of curvature?

  1. $100 cm$
  2. $25 cm$
  3. $50 cm$
  4. $400 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
We know,
$ Focal\ length\ (f) = \dfrac{Radius\ of\ curvature\ (R)}{2} $

$ \Rightarrow Radius\ of\ curvature\ (R) = 2 \times Focal\ length\ (f) $

Given, 
Focal Length, $ f = 200\ cm $
$ \Rightarrow R = 2 \times f = 2 \times 200 = 400\ cm $
$ \Rightarrow Radius\ of\ curvature\ (R) = 400\ cm $

Hence, the correct answer is OPTION D.
Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

A spherical mirror has radius of curvature equal to $50 cm$. Find the value of focal length.

  1. $50 cm$
  2. $30 cm$
  3. $25 cm$
  4. $100 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We know,
$ Focal\ length\ (f) = \dfrac{Radius\ of\ curvature\ (R)}{2} $

Given, 
Radius of curvature, $ R = 50\ cm $
$ \Rightarrow f = \dfrac{R}{2} = \dfrac{50}{2} = 25\ cm $
$ \Rightarrow  Focal\ length\ (f) = 25\ cm $

Hence, the correct answer is OPTION C.

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

An object is at a distance of  $10cm$  from a concave mirror and the image of the object is at a distance of  $30\mathrm { m }$ from the mirror on the same side as that of the object. The radius of curvature of the concave mirror is

  1. $+ 15.0 \mathrm { cm }$
  2. $+ 7.5 \mathrm { cm }$
  3. $- 7.5 \mathrm { cm }$
  4. $- 15.0 \mathrm { cm }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

A real image of half the size is obtained in a concave spherical mirror with a radius of curvature of $40 cm$, the distance of object and its image will be

  1. $30 cm\quad and \quad 60cm$
  2. $60 cm\quad and \quad 30cm$
  3. $15 cm\quad and \quad 30cm$
  4. $30 cm\quad and \quad 15cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Lets, $u=$ object distance
$v=$ image distance
Given, 
$R=40cm$
$f=\dfrac{R}{2}=20cm$
magnification, $m=\dfrac{h}{2h}=\dfrac{v}{u}$ (for real image)
$v=\dfrac{u}{2}$. . . . (1)
By mirror formula,
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$
$\dfrac{1}{20}=\dfrac{2}{u}+\dfrac{1}{u}$
$u=60cm$
From equation (1),
$v=\dfrac{60}{2}=30cm$
The correct option is B.
Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

What will be the height of image when an object of $2\ mm$ is placed at a distance $20 \ cm$ infront of the axis of a convex mirror of radius of curvature $40\ cm$ ?

  1. $20\ mm$
  2. $10\ mm$
  3. $6\ mm$
  4. $1\ mm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\begin{array}{l} \dfrac { 1 }{ V } +\dfrac { 1 }{ \mu  } =\dfrac { 1 }{ f }  \ \dfrac { 1 }{ V } =\dfrac { 1 }{ { 10 } } ,V=10cm \end{array}$

Height of object
$\begin{array}{l} =2mm=\dfrac { 1 }{ 5 } cm \ \dfrac { { Hi } }{ { Ho } } =\dfrac { V }{ 4 }  \ \dfrac { { Hi } }{ { 1/5 } } =\dfrac { { 10 } }{ { -20 } } \Rightarrow Hi=-\dfrac { 1 }{ { 10 } }  \ 1mm\, \, above\, \, axis \end{array}$

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

An object is placed at 15 cm from a convex lens of focal length 10 cm . Where should another convex mirror of radius 12 cm placed such that image will coincide with object

  1. 18 cm

  2. 17 cm

  3. 14 cm

  4. 20 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, find the image position from the lens: 1/v - 1/-15 = 1/10 => 1/v = 1/10 - 1/15 = 1/30. v = 30 cm. For the mirror to make the image coincide, the light must strike the mirror normally, meaning the image must be at the center of curvature. Mirror R = 12, so C = 12. Distance = 30 - 12 = 18 cm.