1. An object\'s distance from a converging lens is 5.61 times the focal length.

Question

1. An object's distance from a converging lens is 5.61 times the focal length. (a) Determine the location of the image. Express the answer as a fraction of the focal length. distance f location (b) Find the magnification of the image. (c) Indicate whether it is upright or inverted. upright inverted (d) Indicate whether it is real or virtual. real virtual

2. The top of a swimming pool is at ground level. If the pool is 2.13 m deep, how far below ground level does the bottom of the pool appear to be located for the following conditions? (a) The pool is completely filled with water. m below ground level (b) The pool is filled halfway with water. m below ground level

3.A person walks into a room that has two flat mirrors on opposite walls. The mirrors produce multiple images of the person. Consider only the images formed in the mirror on the left. When the person is 2.50 m from the mirror on the left wall and 5.30 m from the mirror on the right wall, find the distance from the person to the first three images seen in the mirror on the left wall. a) first image b) second image c)third image

Explanation / Answer

An object's distance from a converging lens is 5.61 times the focal length it means that,

d0 = 5.61 f

using the lens formula,

1 / di + 1 / d0 = 1 / f                              { eq. 1 }

1 / di = 1 / f - 1 / d0

inserting the values in eq.

1 / di = 1 / f - 1 / 0.561 f = 1 / f [ 1 - 0.561 ] = (0.439 / f )

di = f / 0.439 = 2.27 f

magnification of the image is given as ::

m = - di / d0                                    { eq. 2 }

inserting the values in eq. 2,

m = - (2.27 f / 0.561 f) = - 4.04

It is Inverted and real.

(b) The refractive index of water is 1.33. So, an object which is 1m below the surface of the water will only appear to be (1m / 1.33) = 0.75m below.

If the pool is 2.13m deep and is completely filled with water, then, the bottom of the swimming pool will appear to be 2.13m x 0.75m = 1.59m below ground.

If the same pool is only half-filled, the surface will appear to be 1.065m below ground and the bottom will appear to be 1.065m x 0.75 = 0.79m below, so the bottom will appear to be 1.065m + 0.79m = 1.85m below ground.

(3) When the person is 2.50 m from the mirror on the left wall and 5.30 m from the mirror on the right wall, then

distance from the person to the first three images seen in the mirror on the left wall is given as :

for a first image :

doubling the distance of the left mirror to the person = 2 x 2.5m = 5m

for a second image :

adding 5m to the image of distance produced on the right mirror = 2 x 5.3m + 5m = 15.6 m

for a third image :

doubling the distance of the left image produced and adding it to the total distance of the second image =

2 x 2.5m + 15.6m = 20.6 m

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