Question

A 3 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 15 cm. the distance of the object from the lens of 20cm find the nature, position and size of the image

Answer 1

Length of object is equal to 3 cm

So according to the formula of the lens 1/f=1/v-1/u

1/15=1/v-1/-20

1/15+1/-20=1/v

4-3/60=1/v

1/60=1/v

V=60cm beyond the lens

Linear magnification m=I/O=v/u=-3

The image formed is real inverted and diminished

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Answer 2

The height of the image is 4.5 cm.

Image distance, v = 30 cm

Explanation:

Given that,

Height of the object, h = 3 cm

The focal length of the convex lens, f = +15 cm

Object distance, u = -20 cm

Let v is the distance between image and the lens. It can be calculated using lens formula as :

$\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}$

$\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{(-30)}$

v = 30 cm

So, the image will be formed at a distance of 30 cm from the lens. The magnification in case of lens is given by :

$m=\dfrac{v}{u}=\dfrac{h'}{h}$

$\dfrac{30}{-20}=\dfrac{h'}{3}$

h' = -4.5 cm

So, the height of the image is 4.5 cm. Hence, this is the required solution.

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Lens formula

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