Question

an object of height 5 cm is placed at a distance of 30 cm from the convex lensfocal length 10 cm the height of image of the object is
a)2cm
b)2.5cm
C)1cm
d)1.5cm​

Answer 1

Given :-

• height of object, h₁ = 5 cm
• position of object, u = - 30 cm
• focal length of convex lens, f = 10 cm

To find :-

• height of image , h₂ = ?

Formula used :-

• Lens formula

       1 / f = 1 / v - 1 / u

• Formula for magnification of lens

       m = v / u = h₂ / h₁

( where u is the position of object , v is the position of image , f is the focal length of lens , m is the magnification , h₂ is the height of image , h₁ is the height of object )

Solution :-

Calculating position of image using Lens formula

→  1 / f = 1 / v - 1 / u

→ 1 / 10 = 1 / v - 1 / (-30)

→ 1 / v = 1 /10 + 1 / (-30)

→ 1 / v = ( 3 - 1 ) / 30

→ 1 / v = 2 / 30

→ v = 15 cm

Calculating height of image using formula for magnification of lens

→ v / u = h₂ / h₁

→ 15 / (-30) = h₂ / 5

→ h₂ = -2.5 cm

Therefore,

Height of image of the object will be 2.5 cm .

(negative sign in h₂ = -2.5 cm shows that image formed is inverted)

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OPTION (b) 2.5 cm is correct