To a person swimming 0.790 m beneath the surface of the water in a swimming pool

Question

To a person swimming 0.790 m beneath the surface of the water in a swimming pool, the diving board directly overhead appears to be a height of 5.10 m above the swimmer.

Part A: What is the actual height of the diving board above the surface of the water?

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A converging lens with a focal length of 11.2 cmforms a virtual image 8.40 mm tall, 17.2 cm to the right of the lens.

Part A:Determine the position of the object.

Part B:Determine the size of the object.

Part C:Is the image erect or inverted?

Part D:Are the object and image on the same side or opposite sides of the lens?

Explanation / Answer

1) The refractive index of water is n = apparent height/actual height of the object

apparent height from the surface = 5.10 - 0.790 = 4.31 m

1.33 = 4.31/actual height

Actual height = 3.24m

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2) A) let u is the object distance.

1/u + 1/v = 1/f

1/u = 1/f - 1/v

1/u = 1/11.2 - 1/(-17.2)

u = 6.78 cm

B) Magnification, m = -v/u

= -(-17.2)/6.78

= 2.54

m = image hight/object height

==> object height = image hight/m

= 8.40/2.54

= 3.31 mm

C) Image is erect

D) the object and image on the same side of the lense. since the image is virtual.

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