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# Geometrical Optics: Lenses, Prism, multiple-total reflection

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1. A Lighted candle (shown) 10.0 cm high is placed 40.0 cm in front of a converging lens with f1= 15 cm, which in turn is 70 cm in front of another converging lens of f2 = +20 cm.

(a) Draw a "good" ray diagram "to scale" ( show focal lengths, etc.) for this problem. Estimate from your diagram the location and size of the final image; (Note, the drawing below is NOT to scale, redraw.......).

(b) Calculate that location and size of the intermediate ( from 1st lens only ) final image.

(c) If now f2= - 20 cm, where is the final image, and what is the final magnification ( and sketch the ray diagram).

2. The diagram below shows a 30-60-90 prism made of glass whose index of refraction is 1.5. The long side, shown in a bolder line, is silvered and acts like a mirror. A ray of light is incident on the short side at an angle of 30 degree, as shown. Assume the prism is surrounded by air. You will need to remember that the sum of the angles in a triangle is 180 degree.

(a) Determine the angle of reflection at point A.

(b) Determine what happens at point B and sketch the path of the ray at B. Show your work.

3. The figure shows four long horizontal layers of different materials, with air above and below the stack. The index of refraction is given for each layer. With the incoming light rays as shown, in which layer is there a possibility of totally trapping the light in that layer, so that, after many reflections, all the light reaches the far end of the layer?
Give the index of the layer & Explain WHY you determined that as you choice.

4. A photographer wishes to take a picture of his pet chicken Fred, who happens to have a fine face 5.0 cm high. While standing 2.0 m away, he selects a lens that will fill the film (24 mm top- to- bottom) with Fred's feathered face. (not to mention the alliteration)
a. Sketch a picture of the optical path for the camera image!
b. What is the focal length of the lens that will create this sized image?

(see diagram in attachment)