A.) an object 1.53 cm high is placed 26.7 cm to the left of converging lens of f

Question

A.) an object 1.53 cm high is placed 26.7 cm to the left of converging lens of focal length 12.2 cm. find the position of the image of this object relative to the lens. ANS= 22.5 cm

B.) a second converging lens of focal length 15.3cm is placed 30.9 cm to the right of the first lens. The image produced by the first lens now becomes the object for the second lens. Find the object distance i.e. the distance between the first image and lens 2.

C.) How far from the second lens is the image that it forms?

D.) What is the height of the final image?  

I have part A, i just need help on B-D

Explanation / Answer

a)

ho = object height = 1.53 cm

do = object distance = 26.7 cm

f = focal length = 12.2 cm

di = image distance

using lens equation

1/di + 1/do = 1/f

1/di + 1/26.7 = 1/12.2

di = 22.5 cm

b)

for second lens :

do = object distance = 30.9 - 22.5 = 8.4 cm

c)

f = focal length = 15.3 cm

di = image distance

using lens equation

1/di + 1/do = 1/f

1/di + 1/8.4 = 1/15.3

di = - 18.6 cm

magnification for first lens = m1 = - di/do = - 22.5 / 26.7 = - 0.84

height of image formed by first lens = hi = m1 ho = ( - 0.84 ) (1.53) = - 1.285 cm

magnification for second lens = m2 = - di/do = - (-18.6) / 8.4 = 2.21

height of image formed by second lens = h'i = m2 hi = 2.21 (- 1.285) = - 2.84

so height of final image = 2.84 cm

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