two lenses In the figure are shown two converging lenses with x2 = 1 m. The lens

Question

two lenses In the figure are shown two converging lenses with x2 = 1 m. The lens on the left (Lens 1) has a focal length of 0.25 m while the one on the right (Lens 2) has a focal length of 0.2 m. An object 2.1 cm high is located x1 = 0.412 m to the left of Lens 1. Make sure to include plenty of significant digits in your answers.

1) Consider the image of the object formed by Lens 1. Give its distance as measured from Lens 1 and the image height. Distance = m Your submissions: 0.635 corect

2) Height = 3.24 - WRONG

3) Now consider the image formed by Lens 1 as the object for Lens 2. Locate the image formed by Lens 2 as measured from Lens 2 and give the height of the image. Distance = 4 WRONG

4) Height = 8.4 WRONG

Explanation / Answer

Thin lens formula: 1/p + 1/q = 1/f
p is positive on the left and q is poitive on the right:

1.
1/0.412 + 1/q = 1/0.25
q = 1/(1/0.25 - 1/0.412) = 0.635 m (to the right of Lens 1)

2.
Magnification m = -q/p = -0.635/0.412 = -1.5412
Height = 2.1*(-1.5412) = -3.2365cm
(The negative sign indicates that the image is upside down)

3.
Distance between Lens1 and Lens 2 is 1 m
Image is 1 - 0.635 = 0.365 m to the left of Lens 2
1/p + 1/q = 1/f
1/0.365 + 1/q = 1/0.2
q = 1/(1/0.2 - 1/0.365) = 0.442 (to the right of Lens 2)

4.
m = -q/p = -0.442/0.365 = -1.210
Height = (-3.2365)*(-1.210) = 3.916 cm
(Image is inverted again, now upright)

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