Two thin lenses are kept coaxially in contact with each other and the focal length of the combination is 80 cm. if the focal length of one lens is 20 cm, the focal length of the other would be

General
1

two thin lenses are kept coaxially in contact with each other and the focal length of the combination is 80 cm. if the focal length of one lens is 20 cm, the focal length of the other would be

2

What is the focal length of the other lens if one lens has a focal length of 20 cm and the combined focal length of two coaxial lenses in contact is 80 cm?

Answer:
When two thin lenses are in contact and coaxial, their combined focal length can be calculated using the formula:

[
\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}
]

Given that the focal length of one lens ( f_1 = 20 , cm ) and the combined focal length ( f = 80 , cm ), we can substitute the values into the formula:

[
\frac{1}{80} = \frac{1}{20} + \frac{1}{f_2}
]

Solving for ( f_2 ):

[
\frac{1}{f_2} = \frac{1}{80} - \frac{1}{20} = \frac{1}{80} - \frac{4}{80} = \frac{3}{80}
]

[
f_2 = \frac{80}{3} = 26.67 \approx 26.7 , cm
]

Therefore, the focal length of the other lens would be approximately ( 26.7 , cm ).