Math, asked by jagadalasritej, 2 months ago

An object is imaged by a lens on
a screen placed 12 cm from the
lens. When the lens is moved 2
cm away from the object, the
screen must be moved 2 cm
closer to the object to reform it.
Find the focal length of the lens.

Answers

Answered by nerellaprasanna25

Answer:

Step-by-step explanation:

Attachments:

Answered by knjroopa

Step-by-step explanation:

Given An object is imaged by a lens on a screen placed 12 cm from the lens. When the lens is moved 2 cm away from the object, the screen must be moved 2 cm closer to the object to reform it. Find the focal length of the lens

Now we have
1/f = 1/v + 1/u
1/12 = 1/f – 1/u
Now the lens is moved 2cm away from the object and screen to be moved 2 cm closer to the screen.
u’ = u + 2
v’ = 12 – 2 – 2
v’ = 8
Now
1/8 = 1/f – 1/u + 2
1/12 = 1/f – 1/u
On subtracting we get
1/8 – 1/12 = 1/u – 1/u + 2
1/24 = 2/u^2 + 2u
u^2 + 2u = 48
u^2 + 2u – 48 = 0
u^2 + 8u – 6u – 48 = 0
u(u + 8) – 6(u + 8) = 0
(u + 8) (u – 6) = 0
Or u = 6, - 8
Considering u = 6 cm we get
1/f = 1/12 + 1/6
= 1 + 2 / 12
= 3/12
1/f = ¼
Or f = 4 cm