A spherical mirror (concave) is placed 24cm to the right of an object. Spherical
ID: 3899206 • Letter: A
Question
A spherical mirror (concave) is placed 24cm to the right of an object.
Spherical Mirror Lesson: Sometimes, I use units of diopters. (Diverging, 4 -1/4m = -25cm) (Converging, 2 1/2m = 50cm) (Diverging, Pizza = A spherical mirror (Concave, 8) is placed 24cm to the right of an object. What is the focal length? What is the radius of the mirror? What is the image distance? Where is the image? Is the image real or virtual? Is the image inverted or not inverted? What is the magnification? Is it enlarged or diminished? Draw the ray diagram with 3 rays.Explanation / Answer
Since we are dealing with a concave mirror, the fact that a real image is formed means that the object is located outside the focal length.
We use the equations:
1/do + 1/di = 1/f
where:
do is the distance between the object and the mirror
di is the distance between the image and the mirror
f is the focal distance
and
M = hi/ho = -di/do
where:
M is the magnification
hi is the height of the image
ho is the height of the object
di is the distance between the image and the mirror
do is the distance between the object and the mirror
a) First we need to calculate the distance between the image and the mirror:
hi/ho = -di/do
di = - hi*do/ho = -11.1 cm * 10.5cm / 4.7cm = -24.7978723 cm
The image is located 24.7978723 cm from the mirror
Plug into the equation:
1/do + 1/di = 1/f
1/f = 1/(10.5 cm) + 1/(24.7978723 cm)
f = (1/(10.5 cm) + 1/(24.7978723 cm))^-1 = 7.37658227 cm
The focal length is half the radius of curvature in a concave mirror.
Thus the radius of curvature is
2*7.37658227 cm = 14.7531645 cm
b) To form a virtual image, the object must be placed within the focal length. The height of the virtual image can be determined by drawing a line from the focus through tip of the object to the mirror. (See second source)
Hence we can derive:
ho/(f-do) = hi/f
do = f - ho*f/hi
do = 7.37658227 cm - (4.7 cm*7.37658227 cm)/11.1 cm
do = 4.25316455 cm
Check: do is less than focal length.
Answer:
a) 14.75 cm
b) 4.25 cm
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