Question

A beam of light converges to a point P. Now a lens is placed on the path of the convergent beam 12 cm
from P. At what point does the beam converge if the lens is

(a) a convex lens of focal length 20 cm, (b) a concave lens of focal length 16 cm​

Answer 1

$\huge\underline\purple{\sf Solution:}$

a) A convex lens of focal Lenght 20cm :-

$\large\underline\pink{\sf Given:- }$

Distance of object from lens (u) = 12 cm

Focal Lenght of convex lens (f) = 20 cm

$\large\underline\pink{\sf To\:Find:- }$

Point at which beam converges (v) = ?

━━━━━━━━━━━━━━━━━━━━━━━━━

According to lens formula :-

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

$\large{\sf {\frac{1}{v}}={\frac{1}{u}}+{\frac{1}{f}}}$

$\large\implies{\sf {\frac{1}{12}}+{\frac{1}{20}}}$

$\large\implies{\sf {\frac{60}{8}}}$

$\large\implies{\sf 7.5cm }$

$\huge\red{♡}$$\large\red{\boxed{\sf v=7.5cm }}$

i.e. , the image is formed on the right of the lens and is real .

━━━━━━━━━━━━━━━━━━━━━━━━━━

b) A concave lens of focal length 16 cm :-

$\large\underline\pink{\sf Given:- }$

Distance of object from lens (u) = 12 cm

focal length of concave lens (f) = 16 cm

$\large\underline\pink{\sf To\:Find:- }$

Point at which beam converges (v) = ?

━━━━━━━━━━━━━━━━━━━━━━━━━

According to Lens Formula :-

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

$\large{\sf {\frac{1}{v}}={\frac{1}{f}}+{\frac{1}{u}}}$

$\large\implies{\sf {\frac{1}{-16}}+{\frac{1}{12}}}$

$\large\implies{\sf +48cm }$

$\huge\red{♡}$$\large\red{\boxed{\sf v=+48cm}}$

i.e., The image is formed at 48 cm to the right of the lens where the beam would converge and is real

Answer 2

❤Bonjour❤

Refer to the attachment!!