Question

A convex lens has focal length equal to 8 cm. An object is placed at a distance 12 cm from the lens. Calculate the image distance and image height if the height of the object is 24 cm . State the nature of the image

Answer 1

Answer :

• position of image is 24 cm at positive principal axis.
• height of image is 48 cm below principal axis.
• nature of image is real and inverted.

Given :

• focal length of convex lens , f = 8 cm
• position of object , u = -12 cm
• height of the object , h₁ = 24 cm

To find :

• position of image, v = ?
• height of image, h₂ = ?
• Nature of the image

Formulae required :

• Lens formula

      1/f = 1/v - 1/u

• Formula for magnification of lens

      m = v/u = h₂/h₁

[ where f is focal length of lens , v is position of image , u is position of object ,m is magnification, h₂ is height of image and h₁ is height of object ]

Solution :-

Using lens formula to calculate position of image

→ 1/f = 1/v - 1/u

→ 1/8 = 1/v - 1/(-12)

→ 1/v = 1/8  - 1/12

→ 1/v = (3 - 2) / 24

→ 1/v = 1 / 24

→ v = 24 cm

Therefore,

image will be formed at 24 cm behind the lens. (i.e, at positive principal axis)

Using formula for magnification of lens to find the height of image

→ m = v/u = h₂ / h₁

→ v / u = h₂ / h₁

→ 24 / (-12) = h₂ / 24

→ -2 = h₂ / 24

→ h₂ = - 48 cm

Therefore,

height of image will be 48 cm below the principal axis.

And,

Nature of image will be real and inverted.