Unit: Optics
Year: 88 Question#: 92
Question: A pencil 0.10 meter long is placed 1.0m in front of a concave (converging) mirror whose focal length is 0.50 meter. The image of the pencil is
(1 ) erect and 0.030 meter long
(2 ) erect and 0.10 meter long
(3 ) inverted and 0.030 meter long
(4 ) inverted and 0.10 meter long
What is this question really asking?
Explanation by: Apia A
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Answer 1
erect and 0.030 meter long
INCORRECT
Using a few formulas to find out image distance and then image length i.e. 1)1/do+1/di=1/f and 2) So/Si=do/di we can conclude two things: 1) the image length is not .030 meter 2) the image length is equal to the object length of .10 meter. We can conclude this, because first we know that do= 1meter f=.5meter using the first equation 1m/1m+1m/di=1m/.5 and so di=1m then using the second equation .1m/Si=1m/1m the image length =.1meter. Therefore this cannot be the correct answer since this answer says the image length is equal to .03m. return to top
Answer 2
erect and 0.10 meter long
INCORRECT
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Answer 3
inverted and 0.030 meter long
INCORRECT
We already know that the image of the pencil is equal in length to the object length (.10 meter) therefore we can conclude that this choice is not a possible answer. return to top
Answer 4
inverted and 0.10 meter long
CORRECT
By process of elimination this is the correct answer but we can also prove this using the physics of optics. For a concave mirror you can draw a line from the object to the mirror then through the focus and then you can also draw a line from the object to the center of the mirror then draw a line at the mirror that is reflected at the same angle. The intersection of these two lines is where the image is located and its size. ( there is a diagram below. ) return to top
What's this question really asking?
What does an image of an object in a concave mirror look like when the object distance is twice the focal length. return to top
