Question

An object 4cm in height b, is placed at 15cm on front of a concave mirror of focal length 10cm .at what distance from the mirror should a screen be placed to obtain Sharp image object . Calculate the height of the image

Answer 1

Given :-

• Height of object (ho) = + 4cm
• Object distance (u) = - 15cm
• Focal length (f) = - 10cm

To find :-

• Image distance (v)
• Height of image (hi)

Solution :-

According to the Mirror Formula

→ 1/v + 1/u = 1/f

→ 1/v + (-1)/15 = -1/10

→ 1/v = 1/15 - 1/10

→ 1/v = 2 - 3/30

→ 1/v = -1/30

→ v = -30cm

According to the Mirror Magnification

★ m = -v/u = hi/ho

→ -v/u = hi/ho

→ -(-30)/-15 = hi/4

→ -2 = hi/4

→ hi = -8cm

Hence,

• Image distance = -30cm
• Height of image = -8cm

Answer 2

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The image height will be 8 cm.

Given-

f = - 10 cm

u = - 15 cm

h₂ = 4 cm

Explanation-

Using the mirror formula,

1/f = 1/v + 1/u

⇒ 1/v + 1/-15 = 1/- 10

⇒ 1/v = 1/- 10 + 1/15

⇒ 1/v = (- 15 + 10)/150

⇒ 1/v = - 5/150

image distance⇒ v = - 30 cm

Magnification-

m = - v/u = h₁/h₂

⇒ m = - 30/- 15

⇒ m = - 2

height of the image⇒ h₁ = - 8 cm