One kind of solar furnace uses a concave mirror to focus parallel rays of sunlig

Question

One kind of solar furnace uses a concave mirror to focus parallel rays of sunlight into a small focal spot, similar to using a magnifying glass to create a small region of intense heat. See a truly astonishing video clip about such a furnace, when the BBC visits the Solar Furnace Research Facility. (YouTube video linked on course schedule.) You decide to construct a solar furnace, using a large spherical mirror with radius of curvature of 190 cm. You use a limited portion of the sphere to keep all angles of incidence at 10 deg and below. If you aim the mirror directly toward the sun, how far away from the vertex will you have to place an object in order to heat it with maximum intensity? The sun's rays are effectively parallel at the distance of Earth. At one moment, a 28 cm bird crosses the mirror's principal axis, 520 cm from the mirror. Where is an image of the bird formed, and how large is the bird's image? Include a ray diagram showing bird and its image. Diagram should agree with your calculated values. You mount a large, flat, 22 cm-thick polycarbonate window just in front of the mirror (between mirror and focal point), normal to the principal axis. The index of refraction of polycarbonate is 1.585. What is the effect of the window on the incoming rays of sunlight? What is the new location of the focal point, compared to its position without the window? Include a ray diagram. Be sure to explain all of your answers as part of your narrative.

Explanation / Answer

a)
sun can be considered to be at infinity
All the rays from infinity will focus at focal point
This is the point of maximum intensity
f = R/2 = 190/2 = 95 cm
Answer: 95 cm

b)
do = 520 cm
f = 95 cm
fo = 28 cm
use:
1/f = 1/di + 1/do
1/95 = 1/di + 1/520
di = 116.2 cm
Image will be formed at a distance of 116.2 cm from mirror

use:
hi/h0 = -di/do
hi/28 = -116.2/520
hi = -6.26 cm
Birds image will be 6.26 cm large
It will be inveerted

Please draw the ray diagram accordingly

c)
I don't think focal length wii change

i am allowed to answer only 1 question at a time

But I have answered 2

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