You wish to create a 3 cm tall image on a screen 45 cm from a 6 cm tall illumina

Question

You wish to create a 3 cm tall image on a screen 45 cm from a 6 cm tall illuminated light bulb. What focal length lens would you use and where would you place it?
Draw the system below (show all calculations) You wish to create a 3 cm tall image on a screen 45 cm from a 6 cm tall illuminated light bulb. What focal length lens would you use and where would you place it?
Draw the system below (show all calculations) You wish to create a 3 cm tall image on a screen 45 cm from a 6 cm tall illuminated light bulb. What focal length lens would you use and where would you place it?
Draw the system below (show all calculations)
Draw the system below (show all calculations)

Explanation / Answer

given,

height of image = 3 cm

distance of image from object = 45 cm

height of object = 6 cm

height of image / height of object = distance of image / distance of object

3 / 6 = di / do

do = 2di ------ (1)

also given that

di + do = 45 -------(2)

on solving 1 and we'll get

di = 15 cm

do = 30 cm

by lens equation

1 / f = 1 / di + 1 / do

1 / f = 1 / 15 + 1 / 30

f = 10 cm

focal length of the lens = 10 cm

lens should be placed at 30 cm from object

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