Question

If an object is placed in front of a lens at distance 40cm from the lens. Find the nature size and position of image? If the power of lens is 2 diopter.​

Answer 1

FINAL ANSWER:-

• image is real and inverted also image is highly magnified

• position of image v=-200 cm

GIVEN:-

• an object is placed in front of a lens at distance (u) ⇒ 40cm

• the power of lens P ⇒ 2 diopter

TO FIND:-

• the nature size (m)

• position of image (v)

FORMULA USED:-

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

$m=\frac{v}{u}$

SOLUTION:-

as power is giver so by using formula we can find lens's focal length.

$P=\frac{1}{f}$

here

P unit is diopter

F is taken in meter

$2=\frac{1}{f}\\f={1}{2}\\f=0.5m \:\:f=+50cm$

here 50 implies that focal length is in positive '+'ve means it is a convex length .

now , let's find position of image

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\\frac{1}{50}=\frac{1}{v}-(\frac{-1}{40})\\\frac{1}{50}=\frac{1}{v}+\frac{1}{40}\\\frac{1}{50}-\frac{1}{40}=\frac{1}{v}\\\frac{4-5}{200}=\frac{1}{v}\\\frac{1}{v}=\frac{-1}{200}\\v=-200$

image is real and inverted (because of '-'ve sign implies that image is form down the principal axis)

$m=\frac{v}{u}$  ⇒ $m=\frac{-200}{40}$  ⇒ $m=-5D$

image is highly magnified

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some other important facts

if focal length is in '-'ve that means it's concave lens or concave mirror

if  focal length is in '+'ve that means it's convex lens or convex mirror

Answer 2

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