Question

An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.

An object 5 cm high is held 25 cm away from a converging lens of focal length 10 cm. Find the position, size and nature of the image formed. Also draw the ray diagram.

Answer 1

Given: Object distance (u) = −25 cm

Object height (h_o) = 5 cm

Focal length (f) = +10 cm

According to the lens formula,

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

⇒ `1/v = 1/f + 1/u`

⇒ `1/v = 1/10 - 1/25`

⇒ `1/v = 15/250`

⇒ v = `250/15`

⇒ v = 16.66 cm

The positive value of v shows that the image is formed on the other side of the lens.

Magnification (m) = `-"Image distance"/"object distance"`

⇒ m = `-v/u`

⇒ m = `16.66/25`

⇒ m = −0.66

The negative sign shows that the image is real and formed behind the lens.

Magnification (m) =`"Image height"/"Object height"`

⇒ m = H_i/H_o` = "H"_i/5`

⇒ H_i = m × H_o

⇒ H_i = −0.66 × 5

⇒ H_i = −3.3 cm

The negative value of the image height indicates that the image is inverted. The position, size, and nature of the image are shown in the following ray diagram.