Tag: reflection of light in spherical mirrors

Questions Related to reflection of light in spherical mirrors

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

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

  1. $+ 15.0 \mathrm { cm }$

  2. $+ 7.5 \mathrm { cm }$

  3. $- 7.5 \mathrm { cm }$

  4. $- 15.0 \mathrm { cm }$

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Correct Option: C

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

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

  1. $6 cm$

  2. $4.5 cm$

  3. $9 cm$

  4. $4 cm$

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Correct Option: B

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

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

  1. $30 cm\quad and \quad 60cm$

  2. $60 cm\quad and \quad 30cm$

  3. $15 cm\quad and \quad 30cm$

  4. $30 cm\quad and \quad 15cm$

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Correct Option: B
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.

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 $Km/h$?

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

  1. $3$

  2. $4$

  3. $5$

  4. $6$

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Correct Option: A
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.

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 ?

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

  1. 5 cm

  2. 7.5 cm

  3. -30 cm

  4. 12.5 cm

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Correct Option: C
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.

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 $40\ cm$ ?

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

  1. $20\ mm$

  2. $10\ mm$

  3. $6\ mm$

  4. $1\ mm$

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Correct Option: D
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
$\begin{array}{l} =2mm=\dfrac { 1 }{ 5 } cm \ \dfrac { { Hi } }{ { Ho } } =\dfrac { V }{ 4 }  \ \dfrac { { Hi } }{ { 1/5 } } =\dfrac { { 10 } }{ { -20 } } \Rightarrow Hi=-\dfrac { 1 }{ { 10 } }  \ 1mm\, \, above\, \, axis \end{array}$

A convexo-concave diverging lens is made of glass of refractive index 1.5 and focal length 24 cm. Radius of curvature for one surface is doubled that of the other. Then radii of curvature for the two surface are (in cm) :

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

  1. 6 , 12

  2. 12, 24

  3. 3, 6

  4. 18, 36

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Correct Option: D

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

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

  1. 18 cm

  2. 17 cm

  3. 14 cm

  4. 20 cm

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Correct Option: A

Your are asked to design shaving mirror assuming that a person keep it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. the reduice of curvature of the mirror would then be 

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. 60 cm

  3. -24 cm

  4. 30 cm

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Correct Option: A

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.

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

  1. 3R

  2. 5R

  3. R

  4. 2R

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Correct Option: A