1. The thin glass shell shown in the figure (Figure 1) has a spherical shape wit

Question

1. The thin glass shell shown in the figure (Figure 1) has a spherical shape with a radius of curvature of 12.5cm , and both of its surfaces can act as mirrors. A seed 3.30mm high is placed 15.0cm from the center of the mirror along the optic axis, as shown in the figure.

A. Calculate the location of the image of this seed.

B. Calculate the height of the image of this seed.

C. Suppose now that the shell is reversed. Find the location of the seed's image.

D. Find the height of the seed's image.

2. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect image with a magnification of 2.20 when the mirror is 1.20cm from a tooth. (Treat this problem as though the object and image lie along a straight line.)

A. What kind of mirror is needed? Use a ray diagram to decide, without performing any calculations.

B. What must be the focal length and radius of curvature of this mirror?

3. A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.45m from the mirror. The filament is 5.75mm tall, and the image is to be 37.0cm tall.

A. How far in front of the vertex of the mirror should the filament be placed?

B. To what radius of curvature shold you grind the mirror?

1. The thin glass shell shown in the figure (Figure 1) has a spherical shape with a radius of curvature of 12.5cm, and both of its surfaces can act as mirrors. A seed 3.30mm high is placed 15.0cm from the center of the mirror along the optic axis, as shown in the figure. A. Calculate the location of the image of this seed. B. Calculate the height of the image of this seed. C. Suppose now that the shell is reversed. Find the location of the seed's image. D. Find the height of the seed's image. 2. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect image with a magnification of 2.20 when the mirror is 1.20cm from a tooth. (Treat this problem as though the object and image lie along a straight line.) A. What kind of mirror is needed? Use a ray diagram to decide, without performing any calculations. B. What must be the focal length and radius of curvature of this mirror? 3. A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.45m from the mirror. The filament is 5.75mm tall, and the image is to be 37.0cm tall. A. How far in front of the vertex of the mirror should the filament be placed? B. To what radius of curvature shold you grind the mirror?

Explanation / Answer

Number 1)

The focal length is half the radius of curvature.

For the first part, the mirror is concave and the focal length will be 6.25 cm

Part A)

1/f = 1/p + 1/q

1/6.25 = 1/15 + 1/q

q = 10.7 cm

Part B)

h'/h = -q/p

h'/3.3 = -(10.7)/15

h' = -2.36 mm (The negative means its inverted)

Part C)

Now the mirror is convex so f = -6.25 cm

1/-6.25 = 1/15 + 1/q

q = -4.41 cm

Part D)

h'/h = -q/p

h'/3.3 = -(-4.41)/15

h' = .971 mm

Number 2)

Part A)

The mirror is concave

Part B)

M = -q/p

2.2 = -q/1.2

q = -2.64 cm

Then for f...

1/f = 1/p + 1/q

1/f = 1/1.2 + 1/-2.64

f = 2.2 cm

R = 2f = 4.4 cm

Number 3)

First M = h'/h

M = 37/.575 = 64.35

64.35 = q/p

64.35 = 8.45/p

p = .131 m (13.1 cm)

Thus the filiment is 13.1 cm from the mirror

Now for R, start by finding f...

1/f = 1/p + 1/q

1/f = 1/13.1 + 1/845

f = 12.9 cm

R = 2f = 25.8 cm

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