Question

The image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object and image distances.

Answer 1

Given

Focal length of the lens f = 20 cm

Height of the image h₁ = 4×h₀(height of the object)

Now from magnification we have

m = (-v)/(u) = (h₁)/(h₀) = (4h₀)/(h₀)

(-v)/(u) = 4

- v = 4 u ------(A)

From lens maker formula we have,

(1/v)-(1/u) = (1/f)

(1/-4u) - (1/u) = (-1/20)

(-1+4)/4u = -1/20

-(3×20)/4 = u

u= -15 cm

Reducing the above found value in (A) we get,

-v = 4 u

v = 4 × 15 = 60 cm  

Answer 2

Aɴꜱᴡᴇʀ

➜ Image distance = 15 cm

_________________

Sᴛᴇᴘꜱ

For a Convex lens : erect image⇒positive magnification

$\large\tt \leadsto{m=\frac{h_I}{h_0}=\frac{v}{u}=4}$

★ Cross multiplying

$\tt{\dashrightarrow\:v=4u}$

☞ By Using Lens Formula :

$\Large\boxed{ \sf\frac{1}{v}-\frac{1}{u}=\frac{1}{f}}$

Given that :

✪ Focal length (f) = 20 cm

✪ Object distance = - u

$\tt{\dashrightarrow\frac{1}{4u}-\frac{1}{-u}=\frac{1}{20}}$

$\tt{\dashrightarrow\frac{3}{4u}=\frac{1}{20}}$

$\tt\pink{\dashrightarrow\:u= 15\:cm}$

Hence, the distance of object from lens is 15 cm

_________________

Uses of Convex lens:-

➠ In spectacles for eyes suffering from hypermetropia.

➠ In the lens combination of camera, telescope, microscope.

_____________________________________