Question

Of the focal length of a convex lens is 20cm and the object distance is 18cm then what is the image distance?
And what is the magnification?

Answer 1

u = - 18 cm

f = + 20 cm

=> 1/f = 1/v - 1/u

=> 1/20 = 1/v + 1/18

=> 1/v = 1/20 - 1/18

=> 1/v = 90 - 10 / 180

=> 1/v = 80/180

=> 1/v = 8/18

=> 1/v = 4/9

=> v = + 9/4 cm

Magnification = - v / u

=> m = - ( 9/4 / - 18 )

=> m = 9/4 / 18

=> m = 9/4 × 18

=> m = 9 × 9 / 2

=> + 40.5

Answer 2

Question:

Of the focal length of a convex lens is 20cm and the object distance is 18cm then what is the image distance?  And what is the magnification?

Answer:

• The distance of the image is 180 cm behind the mirror.
• The magnification of the image is 10.

Given:

The focal length of the lens is 20 cm.

The distance of the object is 18 cm.

To find:

• The distance of the image.
• The magnification of the image.

Explanation:

Focal length(f) = 20 cm.

The distance of the object(u) = 18 cm.

Let, the distance of the image be, 'v'.

We know that,

$\frac{1}{f} = ( \frac{1}{u} + \frac{1}{v})$

⇒ $\frac{1}{20} = ( \frac{1}{18} + \frac{1}{v})$

⇒ $(\frac{1}{20} - \frac{1}{18}) = \frac{1}{v}$

⇒ $\frac{1}{v} = ( \frac{1}{20}-\frac{1}{18})$

⇒ $\frac{1}{v} = (\frac{9-10}{180} )$ [∵ The L.C.M. of the denominators is 180.]

⇒ $\frac{1}{v} = -\frac{1}{180}$

⇒ v = - 180 cm.

∴ The distance of the image is 180 cm behind the mirror.

Let, the magnification of the image be, 'm'.

We know that,

$m = - (\frac{v}{u})$

⇒ m = $-(\frac{-180}{18})$

⇒ m = - ( - 10)

⇒ m = 10.

∴ The magnification of the image is 10.

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If the focal length of a convex lens is 20cm and the object distance is 18cm then what is the image distance?  And what is the magnification?

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