1. A concave spherical mirror has a radius of curvature of 29.4 cm. The object distance is 5.7 cm . Find the magnitude of the image distance. Answer in units of cm.
2. Find the magnification.
f=1/2 r=14.7cm
1/o+1/d=1/f solve for d
To find the magnitude of the image distance in a concave spherical mirror, we can use the mirror formula:
1/f = 1/do + 1/di
where f is the focal length of the mirror, do is the object distance, and di is the image distance.
Given:
Radius of curvature (R) = 29.4 cm
Object distance (do) = 5.7 cm
First, we need to find the focal length (f) using the formula:
f = R/2
Substituting the values, we get:
f = 29.4 cm / 2 = 14.7 cm
Now we can substitute the values of f and do into the mirror formula:
1/14.7 cm = 1/5.7 cm + 1/di
Simplifying the equation, we get:
1/di = 1/14.7 cm - 1/5.7 cm
To find the magnitude of di, we take the reciprocal of both sides of the equation:
di = 1 / (1/14.7 cm - 1/5.7 cm)
Now, let's calculate di using a calculator or math software:
di = 10.62 cm (rounded to two decimal places)
Therefore, the magnitude of the image distance is approximately 10.62 cm.
To find the magnification (M), we can use the magnification formula:
M = -di/do
where M represents the magnification, di is the image distance, and do is the object distance.
Given:
di = 10.62 cm
do = 5.7 cm
Substituting the given values, we have:
M = -10.62 cm / 5.7 cm
Calculating the magnification:
M = -1.86 (rounded to two decimal places)
Therefore, the magnification is approximately -1.86.