A convex spherical mirror has a radius of curvature of 50 cm. Determine the position and magni�cation of the image of an object located 35 cm in front of the mirror.
i only know how to do concave mirrors. i have the equations as 1/f=1/d0+1/di for position and m=hi/h0=-di/d0 but idk how to use them in this problem.
ket naxu
No problem! The equations you mentioned, 1/f = 1/do + 1/di for the position and m = hi/ho = -di/do for the magnification, can also be used for convex mirrors. Let's go through the problem step by step.
Given:
- Radius of curvature (R) = 50 cm
- Object distance (do) = -35 cm (negative because the object is located in front of the mirror)
First, let's find the focal length (f):
For a convex mirror, the focal length is negative and given by f = R/2.
Thus, f = 50 cm/2 = -25 cm.
Now, let's find the image distance (di):
Using the equation 1/f = 1/do + 1/di, we can rearrange it to solve for di:
1/di = 1/f - 1/do
1/di = 1/-25 - 1/-35 (substituting the given values)
1/di = -1/25 + 1/35
1/di = (-35 + 25)/(25*35)
1/di = -10/(25*35)
1/di = -10/875
di = -875/10
di = -87.5 cm
Since the image distance (di) is negative, the image formed is a virtual image. It means that the image appears on the same side as the object (behind the mirror).
Next, let's find the magnification (m):
Using the equation m = hi/ho = -di/do:
m = -di/do
m = (-(-87.5))/(35)
m = 87.5/35
m = 2.5
The positive value of the magnification tells us that the image formed is upright, but since it is greater than 1, it is also magnified.
Therefore, the position of the image is 87.5 cm behind the convex mirror, and the magnification is 2.5.