Question

A 2.7-cm-tall object is 20 cm to the left of a lens with a focal length of 10 cm . A second lens with a focal length of 48 cm is 52 cm to the right of the first lens.

A. Calculate the distance between the image and the second lens.B.Calculate the image height.

Answer 1

given,

height of object = 2.7 cm

distance left of lens (u₁)= 20 cm

focal length of lens(f₁)= 10 cm

the distance of image

`(1)/(f_1)=(1)/(u_1)+(1)/(v_1)`

`(1)/(v_1)=(1)/(f_1)-(1)/(u_1)`

`(1)/(v_1)=(1)/(10)-(1)/(20)`

v₁ = 20 cm

magnification of first lens

`m_1= -(v)/(u)`

`m_1=-(20)/(20)`

m₁ = -1

distance of object from the second lens

u₂ = 52-20 = 32 cm

f₂ = 48 cm

now,

`(1)/(f_2)=(1)/(u_2)+(1)/(v_2)`

`(1)/(v_2)=(1)/(f_2)-(1)/(u_2)`

`(1)/(v_2)=(1)/(48)-(1)/(52)`

v₁ = 624 cm

magnification of first lens

`m_1= -(v)/(u)`

`m_1=-(624)/(52)`

m₁ = -12

total magnification

m = m₁ m₂

m = (-1)(-12)

m = 12

height of image

`m =-(h')/(h)`

`12=-(h')/(2.7)`

h' = -32.4 cm

a) distance between image and second lens is equal to 624 cm

b) height of image is equal to 32.4 cm