CE Physics MC 2004 Q15

用戶199399

2007-07-30 7:56 am

An object is placed in front of a convex mirrior. Which of the following statements about the properties of the image formed in the mirrior must be correct?
(1) The image is diminished
(2) The image is virtual
(3) The image distance is smaller than the focal length of the mirrior
A. (1) and (2) only
B. (1) and (3) only
C. (2) and (3) only
D. (1), (2) and (3)
Why the answer is D, but not C?

回答 (1)

魏王將張遼

2007-07-30 5:44 pm

✔ 最佳答案

First of all, the ray diagram for formation of image in convex lens is shown below:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Jul07/Crazyoptic1.jpg

Above is the visual proof for statement (3).
Mathematically, we can prove it in accordance to the formula:
(1/f) = (1/u) + (1/v)
where
f = focal length (Negative for a convex mirror)
u = Object distance (Must be positive)
v = Image distance (Negative for virtual image)
Changing the expression, we have:
(1/v) = (1/f) - (1/u)
So to speak, we have the following deductions:

(1/v) is MORE NEGATIVE than (1/f)
|1/v| > |1/f| (Absolute value)
|v| < |f| (since it must be positive)
Hence, we can see that the absolute value of v is smaller than that of f, i.e. the image distance is smaller than the focal length of the mirror.
(Note: This topic is already out C in CE physics now.)

參考: My physics knowledge

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