The thin glass shell shown in (Figure 1) has a spherical shape with a radius of

Question

The thin glass shell shown in (Figure 1) has a spherical shape with a radius of curvature of 10.0 cm , and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm 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.

Express your answer in centimeters to three significant figures.

b)Calculate the height of the image of this seed.

Express your answer in millimeters to three significant figures.

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

Express your answer in centimeters to three significant figures.

d)Find the height of the seed's image.

Express your answer in millimeters to three significant figures

Explanation / Answer

I case

R = 10cm so f = R/2 = 5cm

In first case it acts like a concave mirror so f = -5cm

u = -15cm

Using mirror formula

1/f = 1/v + 1/u

Where

f is focal length

v is image's distance

u is object's distance

Substituting values

1/-5 = 1/v + 1/-15

v= -7.5cm

Using formula for magnification

m = -v/u = -(-7.5)/-15 = -0.5 = hi/ho

where

hi is height of image

ho is height of object

so

-0.5= hi/3.30

hi = -1.65 mm

II case

In this case mirror will act like convex mirror

So focal length will be positive f= 5cm

Using mirror formula again

1/5 = 1/v + 1/-15

v= 3.75 cm

Using formula for magnification

m = -v/u = -(3.75)/-15 = 0.25 = hi/ho

so

0.25= hi/3.30

hi = 0.825 mm

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