Question

the image of a candle flame placed at a distance of 36cm from a spherical lens is is formed on a screen placed at a distance of 72 cm from the lens identify the type of length and calculate its focal length .the height of candle flame is 2.5cm find the height of the image .​

Answer 1

⟶ Given :-

Object distance, u = 36cm

image distance, v = 72cm

object height, h = 2.5cm

⟶ To find :-

Focal length, f

the height of the image, h' .

⟶ Solution :-

It is convex len.

Using lens formula,

.i.e.,

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

$\sf \Longrightarrow\dfrac{1}{72} + \dfrac{1}{36} = \dfrac{1}{f}$

$\sf \Longrightarrow\dfrac{1 + 2}{72} = \dfrac{1}{f}$

$\sf \Longrightarrow\dfrac{3}{72 } = \dfrac{1}{f}$

$\sf\Longrightarrow \dfrac{1}{f} = \dfrac{1}{24}$

$\bf\Longrightarrow \boxed{ \bf f = 24cm}$

hence, focal length is 24cm

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

$\sf \dfrac{72}{ - 36} = \dfrac{h'}{2.5}$

$\sf h' = \dfrac{72 \times 2.5}{ - 36}$

$\bf h' = - 5cm$

thus, the height of the image is -5cm