Question

An object of height 3cm is placed at 10cm from a concave lens of focal length 15cm.find the size of the image​

Answer 1

Answer:

Height of object, h = 3cm.

focal length , f = -15cm.

object distance, u = 10cm.

by the lens formula,

1/f = 1/v - 1/u

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

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

1/v = -3+1/-30

1/v = -2/-30

1/v = 15cm.

size of object,

m = h'/h = -v/u

h' = 3×-15/-10

h' = 9/2

h' = 4.5cm

so the size or height of object is 4.5cm.

Explanation:

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Answer 2

The size of the image is 1.8 cm.

Explanation:

It is given that,

Height of the object, h = 3 cm

Object distance, u = -10 cm

Focal length of the concave lens, f = -15 cm (it has negative sign)

Let v is the distance between lens and the image. Using lens formula to find it as :

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

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

$\dfrac{1}{v}=\dfrac{1}{(-15)}+\dfrac{1}{(-10)}$

v = -6 cm

If h' is the size of the image. It can be calculated using the formula of magnification as :

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

$\dfrac{-6}{-10}=\dfrac{h'}{3}$

h' = 1.8 cm

So, the size of the image is 1.8 cm. Hence, this is the required solution.

Learn more,

Lens formula

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