Question

Find the position and nature of the image of an object 5 cm high and 10 cm in front of a convex lens of focal length 6 cm.

Answer 1

Given: Height of the object (h) = 5 cm

Object distance (u) = −10 cm

Focal length (f) = 6 cm

Applying the lens formula, we get:

`1/f = 1/v - 1/u`

⇒ `1/6 = 1/v - (1/-10)`

⇒ `1/6 = 1/v + 1/10`

⇒ `1/v = 1/6 - 1/10`

⇒ `1/v = (5 - 3)/30`

⇒ `1/v = 2/30`

⇒ `1/v = 1/15`

⇒ v = 15 cm

The positive sign means that the image is formed at a distance of 15 cm on the other side of the lens.

To find the nature and height of the image, calculate the linear magnification (m).

m = `v/u`

⇒ m = `h_i/h_o`

⇒ m = `15/-10`

⇒ m = −1.5

Now, calculate the height of the image (h_i) using the magnification formula:

h_i = m × h_o

h_i = −1.5 × 5

h_i = −7.5

The image is real, inverted and magnified with a total height of 7.5 cm.