Question

an object of height 4 cm is placed at a distance of 15 CM in front of concave lens of power minus 10 diopter find the size of image please give correct answer (unecessary answers will be ignored)​

Answer 1

Answer :-

Size of the image is 1.6 cm .

Explanation :-

We have :-

→ Height of the obejct (hₒ) = 4 cm

→ Distance of object (u) = 15 cm

→ Power of lens (P) = -10 D

______________________________

According to sign convention, we have :-

• u = -15 cm

Focal length of the lens will be :-

⇒ f = 100/P

⇒ f = 10/(-10)

⇒ f = -10 cm

Now, let's calculate the distance of the image (v) by using lens formula .

1/v - 1/u = 1/f

⇒ 1/v = 1/f + 1/u

⇒ 1/v = -1/10 + (-1)/15

⇒ 1/v = (-3 - 2)/30

⇒ 1/v = -5/30

⇒ v = 30/(-5)

⇒ v = -6 cm

______________________________

Now, size of the image according to formula of magnification of lenses will be :-

m = v/u = hᵢ/hₒ

⇒ v/u = hᵢ/hₒ

⇒ -6/(-15) = hᵢ/4

⇒ -24 = -15hᵢ

⇒ hᵢ = 24/15

⇒ hᵢ = 1.6 cm

Answer 2

Given :-

An object of height 4 cm is placed at a distance of 15 CM in front of a concave lens of power minus 10 diopter

To Find :-

find the size of the image

Solution :-

We know that

If the image distance and object distance are in cm. Then

F = 100/P

F = 100/-10

F = -100/10

F = -10 cm

Now

1/f = 1/v - 1/u

1/-10 = 1/v - 1/-15

-1/10 = 1/v + 1/15

-1/10 - 1/15 = 1/v

-3 - 2/30 = 1/v

-5/30 = 1/v

-1/6 = 1/v

6(1) = -1(v)

6 = -v

-6 = v

Now

Magnification = hi/ho = v/u

hi/4 = -6/-15

hi/4 = 6/15

hi = 6/15 × 4

hi = 24/15

hi = 8/5

hi = 1.6 cm