A thin lens with a focal length of 5.71 cm has a firefly sitting 13.9 cm in fron

Question

A thin lens with a focal length of 5.71 cm has a firefly sitting 13.9 cm in front of it. The height of the firefly is 6.11 mm and 58.5 cm on the other side of lens A is a thin lens B that has a focal length of 28.1 cm and shares a common axis.

Please show a diagram and step by step solving process!

A thin lens with a focal length of 5.71 cm has a firefly sitting 13.9 cm in front of it. The height of the firefly iS 6.11 mm and 58.5 cm on the other side of lens A is a thin lens B that has a focal length of 28.1 cm and shares a common axis. s the final image (of lens B) real or virtual? eal Virtual What is the position of the final image relative to the lens B as a positive number? Number cm How high is the image as a positive number? Number Is the final image upright or inverted in relation to the firefly? O Upright O Inverted

Explanation / Answer

lens equation
1/f = 1/p + 1/q

1/5.71 = 1/13.9 + 1/q

q = 9.69cm

Since the lenses are 58.5 cm apart, this image is the object for the second lens and 58.5 - 9.69= 48.81 cm in front of it

thin lens equation for lens B

1/28.1 = 1/48.81+ 1/q

q = 66.22 cm

overall magnification of two lens is M = ( -q/p )( -q/p)

M= ( -9.69/13.9 )(- 66.22/48.81) = 0.945

The relation between magnification and height is

M = h'/h

h' = Mh

h' = (0.945)(6.11 mm) = 5.774 mm

Since the overall magnification is positive, the image is upright and real

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