Question

a) In front of spherical concave mirror of radius 26cm, you position an object of height 2.6cm somewhere along the principal axis. The result image has a height of 0.8cm. How far from the mirror is the object located?

b) In front of a spherical convex mirror of radius 26cm, you position an object of height 2.6cm somewhere already no the principal axis. The resultant image has a height of 0.8cm. How far from the mirror is the object located?

c) On one side of a converging lens of focal length 10cm, you position an object of height 1cm somewhere along the principal axis. The resultant image has a height of 0.3cm. How far from the lens is the object located?

d) On one side of a diverting lens of focal length 10cm, you position an object of height 1cm somewhere along the principal axis. The resultant image has a height of 0.3cm. How far from the lens is the object located?

Answer 1

a). Radius of Concave Mirror, R= 26cm (It will be positive since radius of concave mirror is positive only)

Then focal length of Concave Mirror, f= R/2= (26/2)cm = 13cm

Object Height, h_o= 2.6cm

Image Height, ( Both signs are used since its not given that image is real or imaginary)

Now if "u" is the distance of object from the mirror and "v" is the distance of image from the mirror,

Then using Magnification formula,

Using given values in above,

  

..........................(1)

then using Mirror Equation,

  

Using equation 1 in above,

Now considering negative value first,

which means that object is imaginary which is not possible. Hence this value is not possible.

Now considering positive value,

(ANS)

b). Radius of Convex Mirror, R= -26cm (It will be negative since radius of convex mirror is negative only)

Then focal length of Convex Mirror, f= R/2= (-26/2)cm = -13cm

Object Height, h_o= 2.6cm

Image Height, ( Positive sign is used since image formed by convex mirror is always imaginary, i.e. always upright)

Now if "u" is the distance of object from the mirror and "v" is the distance of image from the mirror,

Then using Magnification formula,

Using given values in above,

  

..........................(1)

then using Mirror Equation,

  

Using equation 1 in above,

(ANS)

c). Focal length of converging lens or conves lens, f= 10cm (It will be positive since focal length of convex lens is positive only)

Object Height, h_o= 1cm

Image Height, ( Both signs are used since its not given that image is real or imaginary)

Now if "u" is the distance of object from the mirror and "v" is the distance of image from the mirror,

Then using Magnification formula,

Using given values in above,

  

..........................(1)

then using Lens Equation,

  

Using equation 1 in above,

Now considering negative value first,

which means that object is imaginary which is not possible. Hence this value is not possible.

Now considering positive value,

(ANS)

d).Focal length of Diverging lens or Concave Lens, f= -10cm (It will be negative since focal length of concave lens is negative only)

Object Height, h_o= 1.0cm

Image Height, ( Positive sign is used since image formed by concave lens is always imaginary, i.e. always upright)

Now if "u" is the distance of object from the mirror and "v" is the distance of image from the mirror,

Then using Magnification formula,

Using given values in above,

  

..........................(1)

then using Lens Equation,

  

Using equation 1 in above,

(ANS)