Question

A concave mirror has a focal length of 63.6 cm.

(a) What is its radius of curvature?

__________ cm

(b) Locate the image when the object distance is 100 cm. (Indicate the side of the mirror with the sign of your answer.)
____________ cm

Describe the properties of the image when the object distance is 100 cm. (Select all that apply.)

A) real

B) virtual

C) upright

D) inverted

(c) Locate the image when the object distance is 10.0 cm. (Indicate the side of the mirror with the sign of your answer.)
________ cm

Describe the properties of the image when the object distance is 10.0 cm. (Select all that apply.)

A) real

B) virtual

C) upright

D) inverted

Answer 1

A.

As

R = 2f

Then

R = 127.2 cm [ANSWER]

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B.

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    63.6   cm
do = object distance =    1.00E+02   cm
di = image distance      
      
Thus, solving for di,      
      
di =    174.725   cm   [ANSWER]

******************

Thus, the magnification, m = -di/do,  
  
m =    -1.747252747

Thus, it is REAL (as di > 0) and INVERTED (as m < 0). [ANSWER]

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Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    63.6   cm
do = object distance =    1.00E+01   cm
di = image distance      
      
Thus, solving for di,      
      
di =    -11.86567164   cm   [ANSWER, PART C]
      
Thus, the magnification, m = -di/do,      
      
m =    1.186567164  

Thus, it is VIRTUAL (as di < 0) and UPRIGHT (as m > 0). [ANSWER]