Question

In: Physics

A certain lens focuses light from an object 2.15 m m away as an image 48.6...

A certain lens focuses light from an object 2.15 m m away as an image 48.6 cm c m on the other side of the lens.

Two converging lenses are placed 30.0 cmcm apart. The focal length of the lens on the right is 20.5 cmcm , and the focal length of the lens on the left is 11.5 cmcm . An object is placed to the left of the 11.5 cmcm focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 11.5 cmcm focal-length lens is the original object?

Expert Solution

1) The lens focuses an image 2.15m away from the lens and forms an image 48.6cm on the other side of the lens. So by sign convention the object distance u = -2.15m = -215cm and image distance v = 48.6cm. If f is the focal length of the lens, then the lens formula is given by

So the focal length of the lens is 39.64cm. Since the focal length id positive, the lens is convex.

2) Given the distance between the two converging lenses d = 30cm, the focal length of the right converging lens f2 = 20.5cm and the focal length of the left converging lens f1 = 11.5cm. An object is placed to the left of the left converging lens. The final image is formed is halfway between the two lenses and is inverted.

Consider the right converging lens first. We know that the final image is formed by the right converging lens. Since the final image is formed halfway between the lens, the distance of final image from right converging lens is d/2 = 15cm.

The final image is inverted so the image is formed on the same side of the object of right converging lens.

So for the right converging lens, by sign convention, v2 = -15cm and f2 = 20.5 cm. By lens formula,

So the object for the right converging lens is 8.66cm from the lens. Since its value is negative the object is in the left side of the right converging lens.

Now consider the left converging lens. The object of the right converging lens is the first image formed by the left converging lens. So the distance of the first image from the left converging lens is (d - 8.66)cm = 21.34cm

So for the left converging lens, by sign convention, v1 = 21.34cm and f1 = 11.5 cm. By lens formula,

So the object is loacted at 24.94cm from the left converging lens. Since its value is negative, the object is on the left side of the left converging lens.

So the original object is 24.94cm to the left of the 11.5cm focal length lens.

genius_generous answered 1 year ago

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