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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

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

  1. 18 cm

  2. 17 cm

  3. 14 cm

  4. 20 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, find the image position from the lens: 1/v - 1/-15 = 1/10 => 1/v = 1/10 - 1/15 = 1/30. v = 30 cm. For the mirror to make the image coincide, the light must strike the mirror normally, meaning the image must be at the center of curvature. Mirror R = 12, so C = 12. Distance = 30 - 12 = 18 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 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

A converging bundle of light rays in the shape of cone with a vertex angle of 45 falls on a circular diaphragm of 20 cm diameter. A lens with power 5 D is fixed in the diaphragm. Diameter of face of lens is equal to that of diaphragm. If the vertex angle of new cone is 

  1. $
    \cfrac { 3 d } { 4 }
    $
  2. $
    \cfrac { 5 d } { 4 }
    $
  3. $
    2 d
    $
  4. $
    \cfrac { 3 } { 2 } d
    $
Reveal answer Fill a bubble to check yourself
B 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

All the following statements are correct except

  1. The magnification produced by a convex mirror is always less than one.

  2. A virtual, crect , same-size image can be obtained by using a plane mirror.

  3. A virtual, crect , magnified image can be formed by using a convex mirror.

  4. A virtual, inverted , same-sized image can be formed by using a convex mirror.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A convex mirror always forms a virtual, erect, and diminished image for any real object position. Therefore, the magnification is always less than 1. Statement A is correct. Statement D is incorrect because a convex mirror cannot form an inverted image for a real object.