Tag: focus and focal length

Questions Related to focus and focal length

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.? 

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

  1. $\dfrac{5}{2}$

  2. $\dfrac{4}{3}$

  3. $\dfrac{5}{3}$

  4. $\dfrac{4}{5}$

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Correct Option: C
Explanation:

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

The focal length of a plane mirror is __________ .

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

  1. positive

  2. negative

  3. zero

  4. infinite

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Correct Option: D
Explanation:

The radius of curvature of a plane mirror is infinite so focal length will also be infinite.

If we say that the focal length of a spherical mirror is $n$ times its radius of curvature, then $n$ must be

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

  1. $2.0$

  2. $1.5$

  3. $0.2$

  4. $0.5$

Show answer
Correct Option: D
Explanation:

since we know that radius of curvature is 2 times focal length i.e R=2f

hence (f=0.5R)

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

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

  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

Show answer
Correct Option: B
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.

State whether true or false.
The focal length of a spherical mirror is double its radius of curvature.

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Focal length of  spherical mirror is half the radius of curvature i.e f $=\cfrac { R }{ 2 } $ .

The focal length of a spherical mirror is ____ its radius of curvature.

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

  1. half

  2. twice

  3. thrice

  4. equal to

Show answer
Correct Option: A
Explanation:

Focal length of  spherical mirror is half the radius of curvature i.e $f =\dfrac R2$

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

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

  1. $100 cm$

  2. $25 cm$

  3. $50 cm$

  4. $400 cm$

Show answer
Correct Option: D
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.

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

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

  1. $50 cm$

  2. $30 cm$

  3. $25 cm$

  4. $100 cm$

Show answer
Correct Option: C
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.

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

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

  1. Plane mirror of small aperture

  2. Spherical mirrors of small aperture

  3. Plane mirrors of large aperture

  4. Spherical mirrors of large aperture

Show answer
Correct Option: B
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.

A concave mirror is made by cutting a portion of a hollow glass sphere of radius $24$ cm. Find the focal length of the mirror.

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

  1. 24 cm

  2. 12 cm

  3. 6 cm

  4. 18 cm

Show answer
Correct Option: B
Explanation:

The radius of curvature of the mirror $=24 cm.$
Thus the focal length
$=24 cm/2$
$=12 cm.$