Tag: focus and focal length

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Questions Related to focus and focal length

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 radii of curvature of the surfaces of a double convex lens are 20 cm and 40 cm respectively, and its focal length is 20 cm. What is the refractive index of the material of the lens.? 

  1. $\dfrac{5}{2}$
  2. $\dfrac{4}{3}$
  3. $\dfrac{5}{3}$
  4. $\dfrac{4}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here $R _1$ = 20 cm, $R _2$ = -40 cm, f = 20 cm
Using lens maker's formula we get,
$\dfrac{1}{20} \, = \, (\mu \, - \, 1) \left ( \dfrac{1}{20} \, + \, \dfrac{1}{40} \right )$
$\dfrac{1}{20} \, = \, (\mu \, - \, 1) \dfrac{3}{40} \, \Rightarrow \, \mu \, = \, \dfrac{5}{3}$

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

Radius of curvature is found to be equal to twice the focal length for:

  1. Plane mirror of small aperture

  2. Spherical mirrors of small aperture

  3. Plane mirrors of large aperture

  4. Spherical mirrors of large aperture
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length. We put this as $R = 2f$. This implies that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.