Question

Some rays falling on a converging lens are
focused 20 cm from the lens. When a
diverging lens is placed in contact with the
converging lens, the rays are for 30 cm from
the combination. What is the focal length of
the diverging lens.
(a)50cm

(b)-50cm

(c)-60cm
(d60cm​

Answer 1

Given:

Parallel rays falling on converging lens are focused at 20 cm from the lens. When a diverging lens is added , the rays are focused at 30 cm from the combination.

To find:

Focal length of diverging lens.

Calculation:

Since the parallel rays upon reflection are getting focussed at a particular distance from the lens , we can consider that distance to be the focal length of the lens.

Therefore , focal length of convex lens alone is 20 cm.

And , focal length of combination of lens is 30 cm.

Let focal length of diverging lens be $f_{2}$

Applying Formula for Combination Of Lens:

$\therefore \: \bold{ \dfrac{1}{f_{eff.}} = \dfrac{1}{f_{1}} + \dfrac{1}{f_{2}} }$

$= > \: \dfrac{1}{( + 30)} = \dfrac{1}{( + 20)} + \dfrac{1}{f_{2}}$

$= > \: \dfrac{1}{f_{2}} = \dfrac{1}{30} - \dfrac{1}{20}$

$= > \: \dfrac{1}{f_{2}} = \dfrac{2 - 3}{60}$

$= > \: \dfrac{1}{f_{2}} = \dfrac{ - 1}{60}$

$= > \: f_{2} = - 60 \: cm$

So , focal length of concave (diverging) lens is -60 cm. Negative value of this type of lens verifies our value.

${\boxed{\bold{\red{\huge{Option \: C}}}}}$

Answer 2

Explanation:

Given Some rays falling on a converging lens are focused 20 cm from the lens. When a  diverging lens is placed in contact with the  converging lens, the rays are for 30 cm from  the combination. What is the focal length of  the diverging lens.

• According to the question we have
• So focal length of converging lens f1 = 20 cm
• We need to find the focal length of diverging lens f2  
• Given rays are 30 cm from the combination so focal length of the combination  f = 30 cm
• So 1/f = 1/f1 + 1/f2
•    1/30 = 1/20 + 1/f2
•   1/30 – 1/20 = 1/f2
•   2 – 3 / 60 = 1/f2
• So – 1/60 = 1/f2
• Or f2 = - 60 cm
• Therefore focal length of the diverging lens is – 60 cm

Reference link will be

https://brainly.in/question/13925721