Physics. Please show work, step by step. When two lenses are used in combination
ID: 1554263 • Letter: P
Question
Physics. Please show work, step by step.
When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A 1.20 cm -tall object is 56.0 cm to the left of a converging lens of focal length 40.0 cm . A second converging lens, this one having a focal length of 60.0 cm , is located 300 cm to the right of the first lens along the same optic axis.
Explanation / Answer
a)
for the first converging lens :
f1 = focal length = 40 cm
do1 = object distance = 56 cm
I1 = image distance = ?
ho1 = object height = 1.20 cm
hi1 = image height = ?
using the lens equation
1/do1 + 1/I1 = 1/f1
1/56 + 1/I1 = 1/40
I1 = 140 cm
using the magnification equation :
m = hi1/ho1 = - I1/do1
hi1/1.20 = - (140)/(56)
hi1 = - 3 cm
140 , - 3
b)
for second lens
f2 = focal length = 60 cm
do2 = object distance = 300 - I1 = 300 - 140 = 160 cm
I2 = image distance = ?
ho2 = object height = hi1 = - 3 cm
hi2 = image height = ?
using the lens equation
1/do2 + 1/I2 = 1/f2
1/160 + 1/I2 = 1/60
I2 = 96 cm
using the magnification equation :
m = hi2/ho2 = - I2/do2
hi2/(-3) = - (96)/(160)
hi2 = 1.8 cm
96 ,1.8