Answer to Question #88987 in Optics for vanshika

Question

An object and screen are 80cm apart. There are two positions at which a convex lens forms real image on the screen the magnification in two cases are 3/2 and 2/3 . calculate the focal length of the lens

Answer 1

We put (8) and (9) in (2):In this case, we can write for convex lens

$$\frac { 1} { d_1} + \frac { 1} { f_1} = \frac { 1} { F} (1)$$

where d is the distance from object to lens, f is the distance from lens to screen, F is the focal length of the lens

Using (1) we got:

$$F=\frac { d_1 f_1} { d_1 + f_1} (2)$$

An object and screen are 80cm apart,

$$d_1 + f_1=0.8 (3)$$

The magnification is given by formula

$$k=\frac { f_1} { d_1} (4)$$

Using (4) we got:

$$k=\frac { 3} { 2} (5)$$

Accordnig to (4) and (5):

$$f_1=1.5 d_1 (6)$$

We put (6) in (3):

$$d_1 + 1.5 d_1=0.8 (7)$$

$$d_1=0.32 (8)$$

Using (6) we got:

$$f_1=0.48 (9)$$

We put (8) and (9) in (2):

F=0.192 m

Answer:

0.192 m