DISTANCE BETWEEN OBJECT AND IMAGE 1. Distance between object and image You have
ID: 1460217 • Letter: D
Question
DISTANCE BETWEEN OBJECT AND IMAGE
1. Distance between object and image You have a thin convex lens with focal length of 20 cm. (a) Suppose you hold your phone's lit-up display 30 cm from one side of the lens. Draw a ray- tracing diagram and use this to determine, graphically. where the image will be formed. (b) Now calculate: How far away from the phone is the image? (Note: I'm asking for the distance between the phone and its image, not the distance between the lens and the image.) And if your phone's screen is 4.5 inches tall, how tall is the image? (c) If you now hold your phone's display 60 cm from the lens on one side, how far away from the phone is the image? (d) If you want the display and a real image of it to be 110 cm from each other, how far from the lens should you hold the phone? (Flint: what does that imply about s and s'?) And how tall is the image? (e) Show that the minimum distance you can get between the phone and a real image of it with this lens is 80 cm. (Hint: express the object-image separation distance as a function of the object distance s and then minimize it.)Explanation / Answer
(a)
Focal length of Convex lens = 20 cm
Distance of Object = 30 cm
1/f = 1/di + 1/do
1/20 = 1/di + 1/30
di = 60 cm
Image will be formed, 60 cm on the other side of lens.
(b)
Distance of Image from object , D = 30 cm + 60 cm
D = 90 cm
Height of Object = 4.5 in
M = hi/ho = -di/do
hi/4.5 = - 60/30
hi = - 9.0
Height of the image, hi = 9.0 inches.
(c)
Now -
Distance of Object = 60 cm
1/f = 1/di + 1/do
1/20 = 1/di + 1/60
di = 30 cm
Distance of Image from Phone , D = 60 cm + 30 cm
D = 90 cm
(d)
Now Distance of Image from Phone , D = 110 cm
di + do = 110 cm
di = 110 - do
1/f = 1/di + 1/do
1/20 = 1/110-do + 1/do
do = 26.3 cm
di = 110 - 26.3
di = 83.7 cm
M = -di/do
hi/4.5 = - 83.7/26.3
hi = -14.32 inch
Height of image, hi = 14.3 inches
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