Question

an object is kept at a distance of 1 m from a convex lens of power 2 dioptre. the image is formed at a distance ______ from the object.​

Answer 1

$\huge {\underline{\pink{Given:-}}}$

• Object distance ,u = -1m = -100cm

• Power of lens ,P = 2D

$\huge {\underline{\green{To Find:-}}}$

• Image distance ,v

$\huge {\underline{\blue{Solution:-}}}$

As we know that the Power of lens is defined as the reciprocal of its focal length in metre.

➺ P = $\frac{1}{focal length (in metre)}$

Substitute the value we get

➺ 2 = 1/f

➺ 2×f = 1

➺ f = 1/2

→ f = 0.5 m

Converting the unit here

1 m = 100cm

Therefore, 0.5m = 0.5 × 100 = 50cm

Now, we have to calculate the image distance .So, using lens formula

• 1/v - 1/u = 1/f

Substitute the value we get

➺ 1/v - 1/(-100) = 1/50

➺ 1/v + 1/100 = 1/50

➺ 1/v = 1/50 - 1/100

➺ 1/v = 2-1/100

➺ 1/v = 1/100

➺ v = 100cm

Therefore, the image formed at a distance of 100 cm from the object.