A certain convex lens is used to create an image of an object that is 2.0 m in f

Question

A certain convex lens is used to create an image of an object that is 2.0 m in front of the lens on a white screen that is 15.0 cm behind the lens. For the sake of clarity in the description that follows, assume that the object, lens, and screen are on the x axis, the lens sits at the origin, and the object is in the positive x direction (so the object, lens, and screen are at x = 2.0 m, x = 0.0, and x = 15 cm respectivly. A second lens is then placed in front of the first at x = 5.0 cm to create an image of an object located at x = 5.0 m on the screen.

5.a. What is the focal length of the first lens?

5.b. Is the second lens convex or concave?

5.c. What is the focal length of the second lens?

5.d. Before the second lens is placed in front of the first, the image of the object at x = 5.0 m exists, it is just not at the plane of the screen. Is this image in front of or behind the screen?

5.e. How far is the image of the object at x = 5.0 m moved to place it on the screen?

Explanation / Answer

From the given question,

a)For the first lens,

object distance(u1)= 2m

image distance (v1)= -15 cm=- 0.15 m

1/v - 1/u= 1/f

1/(-0.15) - 1/2= 1/f

f=6/43 = -0.14 m

The focal length of first lens is 14cm (approx).

b)Since the image is formed behind the objct, it is convex lens.

c)For second lens,

object distance, u2=1.95

image distance, v2=4.95

1/v-1/u=1/f

1/4.95 - 1/1.95=1/f

f=3.21 m

focal length of second lens is 3.21 m

d) The image is virtual and formed behind the screen.

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