When two lenses are used in combination, the first one forms an image that then

Question

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 1.60cm -tall object is 60.0cm to the left of a converging lens of focal length 40.0cm . A second converging lens, this one having a focal length of 60.0cm , is located 300cm to the right of the first lens along the same optic axis.

A.Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0cm .

B.I1 is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

Explanation / Answer

A . Considering the first lens,

u=-60cm f=40cm Ho= 1.6 cm

1/v = 1/f + 1/u = 1/40 - 1/60 =1/120

=> v=120 cm (to the right of first lens)

Height of image I1 = v/u x Ho = 120/-60 x Ho = -2 x 1.6 = -3.2cm

The height of the image is 3.2 cm and the image is inverted.

B . Now, Considering the second lens :

u=-180cm f=60cm

1/v = 1/f +1/u = 1/60 - 1/180 =1/90

v=90cm (to the right of second lens)

Height of final image : v/u x Hi1 = 90/-180 x -3.2 = -0.5 x -3.2 = 1.6 cm

The final image is formed at 90cm to the second lens or 390cm right to the first lens. Its height is 1.6cm and it is erect

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