Please show all work, label all units, explain steps, and cite principles/laws u

Question

Please show all work, label all units, explain steps, and cite principles/laws used.

Mirrors Lenses (a) A dentist uses a spherical mirror to examine a tooth. The tooth is 1.0 cm in front of the mirror, and the image is formed 10.0 cm behind the mirror. What is the radius of curvature of the mirror? (b) What is the magnification of the tooth's image? (c) A slide projector uses a converging lens with a focal length of 105 mm. If a slide is placed 108 mm from the lens, what must the distance between the screen and lens be in order to focus the projected image? (d) If the slide is 24 mm by 36 mm, what are the dimensions of its image?

Explanation / Answer

o = 1 cm ; i = -10 cm ;

we know from lens eqn

1/f = 1/i + 1/o

f = o x i/(o + i) = 1 x -10/(1 - 10) = -10/-9 = 1.11 cm

R = 2f = 2 x 1.11 = 2.22 cm

Hence, R = 2f.

b)M = -i/o = -(-10)/1 = 10

Hence, M = 10

c)f = 105 mm ; o = 108 mm

from lens eqn, we get

i = o x f/(o - f)

i = 105 x 108/(108 - 105) = 3780 mm

Hence, the screen should be at i = 3780 mm

d)h = 24 mm

M = h'/h = -i/o = 3780/108 = 35

h' = 35 x 24 = 840 ; 35 x 36 =

Image dimentions = 840mm x 1260 mm

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