1. An object 5 cm high forms a virtual image of 1.25 cm high, when pla

1.	1. An object 5 cm high forms a virtual image of 1.25 cm high, when placed in front of a convexmirror at a distance of 24 cm. Calculate : (i) the position of the image, (ii) the focal length ofthe convex mirror
Answer» Given:- → Height of the object = 5 cm → Height of the image = 1.25 cm → Distance of the object = 24 cm To find:- → Position of image. → Focal LENGTH of the convex MIRROR. Solution:- We know that :- m = -(v/u) = hᵢ/hₒ ⇒ -(v/u) = hᵢ/hₒ ⇒ -v/(-24) = 1.25/5 ⇒ -24(1.25) = 5(-v) ⇒ -30 = -5v ⇒ v = -30/-5 ⇒ v = 6 cm Hence, the image is formed at a distance of 6 cm from the mirror. The positive sign of v shows that the image is formed on the right i.e. behind the mirror. ________________________________ Since the mirror is convex, we have :- • u = -24 cm Now, according to mirror formula :- 1/v + 1/u = 1/f ⇒ 1/6 + 1/(-24) = 1/f ⇒ 1/6 - 1/24 = 1/f ⇒ [4 - 1]/24 = 1/f ⇒ 3/24 = 1/f ⇒ 3f = 24 ⇒ f = 24/3 ⇒ f = 8 cm Thus, focal length of the mirror is 8 cm .

1. An object 5 cm high forms a virtual image of 1.25 cm high, when placed in front of a convexmirror at a distance of 24 cm. Calculate : (i) the position of the image, (ii) the focal length ofthe convex mirror

Answer»

Given:-

→ Height of the object = 5 cm

→ Height of the image = 1.25 cm

→ Distance of the object = 24 cm

To find:-

→ Position of image.

→ Focal LENGTH of the convex MIRROR.

Solution:-

We know that :-

m = -(v/u) = hᵢ/hₒ

⇒ -(v/u) = hᵢ/hₒ

⇒ -v/(-24) = 1.25/5

⇒ -24(1.25) = 5(-v)

⇒ -30 = -5v

⇒ v = -30/-5

⇒ v = 6 cm

Hence, the image is formed at a distance of 6 cm from the mirror. The positive sign of v shows that the image is formed on the right i.e. behind the mirror.

________________________________

Since the mirror is convex, we have :-

• u = -24 cm

Now, according to mirror formula :-

1/v + 1/u = 1/f

⇒ 1/6 + 1/(-24) = 1/f

⇒ 1/6 - 1/24 = 1/f

⇒ [4 - 1]/24 = 1/f

⇒ 3/24 = 1/f

⇒ 3f = 24

⇒ f = 24/3

⇒ f = 8 cm

Thus, focal length of the mirror is 8 cm .