Question

An object at 5.0 cm in length is placed at a distance of 20cm in front of a convex mirror of radius of curvature 30cm. Find the position of the image,it's nature and size​

Answer 1

Given :

• Distance of object from mirror (u) = -20 cm
• Height of object (H₀) = 5 cm
• Radius of curvature (R) = 30 cm
• Focal length (F) = 15 cm

To Find :

We have to find the position,nature and size of the image

Explanation :

We know the mirror formula,

⇒ 1/F = 1/u + 1/v

→ 1/v = 1/F - 1/u

→ 1/v = 1/15 - (1/-20)

→ 1/v = 4 - (-3)/60

→ 1/v = 7/60

→ v = 60/7

→ v = 8.57

The image is formed at a distance of 8.57 cm behind the convex mirror. Thus, it is virtual and erect.

$\rule{200}{2}$

Now,

⇒ m = -v/u

→ m = -8.57/-20

→ m = 0.4

$\rule{150}{2}$

⇒ m = H₁/H₀

→ 0.4 = H₁/5

→ H₁ = 5 × 0.4

→ H₁ = 2 cm

Thus, the height of an image is 2 cm.

Thus, we can say that that image is diminished.