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Questions Related to physics

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.

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 dobleconves lens of focal length $6 cm$ is made of glass of refractive index $1.5$ the radius of curvature of of one surface is double that of other surface. The value of small radius of curvature is

  1. $6 cm$
  2. $4.5 cm$
  3. $9 cm$
  4. $4 cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Lens maker's formula: 1/f = (n-1)(1/R1 - 1/R2). Given f=6, n=1.5, R1=x, R2=-2x (double-convex). 1/6 = (0.5)(1/x + 1/2x) = 0.5(3/2x) = 3/4x. So 4x = 18, x = 4.5 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 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

image of an object approching a convex mirror of radius of curvature 20 m along its optical axis so is observed to move from $\dfrac{25}{3}$ m to $\dfrac{50}{7}$m into 30s. what is the speed of the object in $Km/h$?

  1. $3$
  2. $4$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$A=20m$  $f=10m.$

From the mirror equation$:$
$\dfrac{1}{{{v _1}}} + \dfrac{1}{{{u _1}}} = \dfrac{1}{f};$
$\frac{1}{{25/3}} + \dfrac{1}{{{u _1}}} = \dfrac{1}{{10}};$
$ = {u _1} =  - 50\,m.$
furthermore$,$ when the picture of the question is at $50/7m.$
$\dfrac{1}{{{V _2}}} + \dfrac{1}{{{u _2}}} = \dfrac{1}{f}$
$\dfrac{1}{{50/7}} + \dfrac{1}{{{u _2}}} = \dfrac{1}{{10}}$
$ = {u _2} = 25m$
contrast out there of the protest$=50-25=25m$
speed$=$ relocation/time
$=25/30$
$5/6 m/sec$
speed in $km/h$ $ = 5/6 \times 18/5$
$ = 3\,km/h.$
Hence,
option $(A)$ is 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 convex mirror of radius of curvature 20 cm forms an image which is half the size of the object.How far is the object from the mirror ?

  1. 5 cm

  2. 7.5 cm

  3. -30 cm

  4. 12.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius of curvature $=20 cm$

So$,$ focal length $=10 cm$
We are given$,$ ${h _o}/2 = {h _i}$
$so,\,{h _o} = 2{h _i}$
$so,\,m = {h _i} = {h _o}$
$m = {h _o}/2{h _o}$
$so,\,m =  - v/u$
$1/2 =  - v/u$
$so,\,u =  - 2v$
By mirror formula$,$ 
$1/f = 1/v + 1/u$
$1/10 = 1/v - \left( { - 1/2v} \right)$
$1/10 = 1/v + 1/2v$
$so,\,1/10 = 2 + 1/2v$
$so,\,1/10 = 3/2v$
$so,\,2v = 30$
$so,\,v = 15\,cm$
$u =  - 2\left( v \right) =  - 30$
Hence,
option $(C)$ is correct answer.