A concave spherical mirror has a radius of curvature of 20.7 cm. Find the locati
ID: 2053593 • Letter: A
Question
A concave spherical mirror has a radius of curvature of 20.7 cm. Find the location of the image for the following object distances. For each case, state whether the image is real or virtual and upright or inverted and find the magnification. (In each case, use the correct sign conventions for all answers. If the image is located at infinity, enter the word infinity for the image distance and for the magnification.)(a) object distance = 40.0 cm
image distance:
Answer in cm.
magnification:
(b) object distance = 19.9 cm
image distance:
Answer in cm.
magnification:
(c) object distance = 10.35 cm
image distance:
Answer in cm.
magnification:
Explanation / Answer
a) object distance = 40cm, focal length = - 20.7/2 = -10.35 cm image distance From 1/f = 1/v + 1/u or I/v = 1/f - 1/u = -1/10.35 - (-1/40) Solving this we get, image distance v = -13. 96 cm magnification = - v/u = - (-13.96/-10.35) = - 1.35 It is real, inverted (b) object distance = 19.9cm From 1/f = 1/v + 1/u or I/v = 1/f - 1/u = -1/10.35 - (-1/19.9) Solving this we get, image distance v = -21.56 cm magnification = - v/u = - (-21.56/-10.35) = - 2.08 It is real, inverted (c) object distance = 10.35 cm From 1/f = 1/v + 1/u or I/v = 1/f - 1/u = -1/10.35 - (-1/10.35) Solving this we get, image distance v = infinity magnification = infinity
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