Question

a needle 10 cm high is placed at 40 cm from a convex lens of focal length 15 cm. Find position, nature and size of image. Also draw ray diagram.

Answer 1

Explanation:

Given,

size of object , H₀ = 4cm

object distance , u = -25cm

focal length of concave mirror , f = -15cm

Use formula ,

1/v + 1/u = 1/f

⇒1/v + 1/-25 = 1/-15

⇒1/v = 1/-15 + 1/25 = (-25 + 15)/375 = 1/-37.5 cm

⇒ v = - 37.5 cm ,

∴ image is formed object side , 37.5cm from pole of concave mirror.

Now, use formula,

Hi/H₀ = -u/v

Where Hi is the size of image .

Now, Hi/4cm = -(-37.5cm)/(-25cm)

Hi = -4 × 37.5/25 cm = -6cm

∴ size of image = 6cm

Hence,sreen should place 37.5 cm left side of mirror and size of image is 6cm .it is inverted and larger than object's size.