Question

At what distance from a concave mirror of focal length 20 cm should an object 2 cm long be placed in order to get an erect image 8 cm tall?​

Answer 1

Answer :-

The object should be placed at a distance of 15 cm from the concave mirror .

Explanation :-

We have :-

→ Focal length (f) = 20 cm

→ Height of object (hₒ) = 2 cm

→ Height of image (hᵢ) = 8 cm

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From the formula of magnification of a spherical mirror, we have :-

m = -(v/u) = hᵢ/hₒ

⇒ -(v/u) = 8/2

⇒ v/u = -4

⇒ v = -4u ---(1)

According to sign convention, we know that f and u are always negative for a concave mirror .

So, now putting values in the mirror formula, we get :-

1/v + 1/u = 1/f

⇒ 1/(-4u) + 1/u = 1/(-20)

⇒ -1/4u + 1/u = -1/20

⇒ (-1 + 4)/4u = -1/20

⇒ 3/4u = -1/20

⇒ -4u = 60

⇒ u = 60/-4

⇒ u = -15 cm

Answer 2

The Object should be placed at a distance of 15 cm from the given concave mirror

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Step by Step Explanation :

Given Data :-

Concave Mirror

☞ Focal Length (f) = 20 cm

☞ Height of Object (h₀) = 2 cm

☞ Height of Image (h¡) = 8 cm

To Find :-

• Object Distance (u)

Solution :-

from the formula of Magnification of a spherical mirror,

m = h¡/h₀ = -(v/u)

⇒ -(v/u) = 8/2 = 4

⇒ v/u = -4

⇒ v = -4u _____eq(1)

According to Sign Convention Rule,

we know that,

• the values of f and u values are always negative for a concave mirror

now, putting the values in mirror formula, we get

1/v + 1/u = 1/f

so,

⇒ 1/(-4u) + 1/u = 1/(-20)

⇒ [(-4u) + u]/(-4u)(u) = 1/-20

⇒ -20 × (-3u) = -4u²

⇒ 60u = -4u²

⇒ 60 = -4u

⇒ u = 60/-4

⇒ u = -15

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• The Object should be placed at a distance of 15 cm from the given concave mirror