Physics

Ray Optics and Mirrors

115 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 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

A spherical surface of radius of curvature $R$ separates air (refractive index 1.0) from glass (refractive index 1.5).The centre of curvature is in the glass. A point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $PQ$ cuts the surface at a point $\mathbf { O } \text { and } \mathbf { P O }= \mathrm { OQ }$.Find the distance of object from the spherical surface.

  1. 3R

  2. 5R

  3. R

  4. 2R
Reveal answer Fill a bubble to check yourself
A 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 $10\mathrm { mm }$ long awl pin is placed vertically In front of a concave mirror. A $5\ mm$ long image of the awl pin is formed at $30\mathrm { cm }$ in front of the mirror, The focal length of this mirror is 

  1. $- 30 \mathrm { cm }$
  2. $- 20 \mathrm { cm }$
  3. $- 40 \mathrm { cm }$
  4. $- 60 \mathrm { cm }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Magnification m = h_i/h_o = -v/u. m = -5/10 = -0.5. -0.5 = -(-30)/u => u = -60. Mirror formula: 1/f = 1/v + 1/u = 1/-30 + 1/-60 = -3/60 = -1/20. f = -20 cm.

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 point object is placed on principal axis of concave mirror of radius of curvature 10 cm at a distance 21 cm from pole of the mirror.  A glass slab of thickness 3 cm and refractive index 1.5 is placed between object and mirror $.$ Find the imaged position of the image formed. 

  1. 4

  2. 3

  3. 16.5

  4. 5
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

The suns diameter is $1.4\times { 10 }^{ 9 }m$ and its distance from the earth is ${ 10 }^{ 11 }m$. The diameter of its image, formed by a convex mirror of focal length 2m will

  1. 0.7 cm

  2. 1.4 cm

  3. 2.8 cm

  4. 10 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a mirror, the magnification m = -v/u = f/(f-u). Given the sun is very far away (u is large), the image is formed at the focus f. The size of the image is h_i = h_o * (f/u). Plugging in values: (1.4 * 10^9) * (2 / 10^11) = 2.8 * 10^-2 m = 2.8 cm.

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 distance of real object when a concave mirror produces a real image of magnification $'m'$ is ($f$ is focal length)

  1. $\left(\frac{m - 1}{m}\right) f$
  2. $\left(\frac{m + 1}{m}\right) f$
  3. $(m-1)f$
  4. $(m+1)f$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a concave mirror, magnification m = f / (f - u). Rearranging for u: m(f - u) = f, mf - mu = f, mu = mf - f, u = f(m - 1) / m. However, for a real image, m is negative. Using m = -|m|, the distance u = f(1 + |m|) / |m|.

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

Converging rays are incident on a convex spherical mirror so that their extensions intersect  $30 cm$  behind the mirror on the optical axis. The reflected rays form a diverging beam, so that their extensions intersect the optical axis  $1.2 m$  from the mirror. The focal length of the mirror is

  1. $40{ cm }$
  2. $60{ cm }$
  3. $30{ cm }$
  4. $24{ cm }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the mirror formula 1/v + 1/u = 1/f. For converging rays, u = +30 cm (virtual object). The reflected rays form a diverging beam with image at v = -120 cm. 1/(-120) + 1/30 = 1/f. 1/f = (-1 + 4) / 120 = 3/120 = 1/40. So f = 40 cm.