The thin glass shell shown in (Figure 1) has a spherical shape with a radius of
ID: 1518638 • Letter: T
Question
The thin glass shell shown in (Figure 1) has a spherical shape with a radius of curvature of 12.5 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. (cm)
B) Calculate the height of the image of this seed. (mm)
C) Suppose now that the shell is reversed. Find the location of the seed's image. (cm)
D) Find the height of the seed's image. (mm)
Explanation / Answer
ANSWER
here,
radius of curvature , r = 12.5 cm
height of seed , ho = 3.3 mm
object distance , do = 15 cm
A)
focal length , f = r/2
f = 6.25 cm
let the image distance be di
using the lens formula
1/f = 1/di + 1/do
1/6.25 = 1/di + 1/15
di = 10.71 cm
the image distance is 10.71 cm
B)
the height of image be hi
hi/ho = -di/do
hi = - 3.3 * 10.71 /15
hi = - 2.36 mm
C)
mirror behaves as convex
focal length , f = - r/2
f = - 6.25 cm
let the image distance be di
using the lens formula
1/f = 1/di + 1/do
- 1/6.25 = 1/di + 1/15
di = - 4.41 cm
the image distance is - 4.41 cm
D)
the height of image be hi
hi/ho = -di/do
hi = 3.3 * 4.41 /15
hi = 0.97 mm
Regards!!!
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