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3 years ago

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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.

1 answer:

irina1246 [14]3 years ago

4 0

Answer

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

$\dfrac{1}{f_1}=\dfrac{1}{u_1}+\dfrac{1}{v_1}$

$\dfrac{1}{v_1}=\dfrac{1}{f_1}-\dfrac{1}{u_1}$

$\dfrac{1}{v_1}=\dfrac{1}{10}-\dfrac{1}{20}$

v₁ = 20 cm

magnification of first lens

$m_1= -\dfrac{v}{u}$

$m_1=-\dfrac{20}{20}$

m₁ = -1

distance of object from the second lens

u₂ = 52-20 = 32 cm

f₂ = 48 cm

now,

$\dfrac{1}{f_2}=\dfrac{1}{u_2}+\dfrac{1}{v_2}$

$\dfrac{1}{v_2}=\dfrac{1}{f_2}-\dfrac{1}{u_2}$

$\dfrac{1}{v_2}=\dfrac{1}{48}-\dfrac{1}{52}$

v₁ = 624 cm

magnification of first lens

$m_1= -\dfrac{v}{u}$

$m_1=-\dfrac{624}{52}$

m₁ = -12

total magnification

m = m₁ m₂

m = (-1)(-12)

m = 12

height of image

$m =-\dfrac{h'}{h}$

$12=-\dfrac{h'}{2.7}$

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

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