A woman holds a tube of lipstick 5.6 cm from a spherical mirror and notices that
ID: 1474489 • Letter: A
Question
A woman holds a tube of lipstick 5.6 cm from a spherical mirror and notices that the image of the tube is upright and half its normal size. (a) Determine the position of the image. Is it in front of or behind the mirror? (Use a negative number below to indicate the image is behind the mirror.)cm
(b) Calculate the focal length of the mirror.
cm
A woman holds a tube of lipstick 5.6 cm from a spherical mirror and notices that the image of the tube is upright and half its normal size. (a) Determine the position of the image. Is it in front of or behind the mirror? (Use a negative number below to indicate the image is behind the mirror.)
cm
(b) Calculate the focal length of the mirror.
cm
(a) Determine the position of the image. Is it in front of or behind the mirror? (Use a negative number below to indicate the image is behind the mirror.)
cm
(b) Calculate the focal length of the mirror.
cm
Explanation / Answer
here,
a)
the image must be half as far away to have half the size,
As it is upright it is a virtual image. i.e the light does not actually pass through this point.
So the point is behind the mirror.
The magnification rule is true for all mirrors and lenses.
the object distance , Do = 5.6 cm
Because any ray which passes through the centre of the lens emerges undeflected then always H/Hi = - Do / Di
Di = Do/2
Di = - 2.8 cm
Di is negative because it is on the other side of the mirror.
the image distance is - 2.8 cm
b)
For the focal length,
1/Do + 1/Di = 1/f
1/5.6 - 1/2.8 = 1/f
f = - 5.6 cm
F is on the far side of the mirror. at position 5.6 cm. Which also means that the mirror surface is convex as seen by the lipstick.
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