- #1
gmmstr827
- 86
- 1
The problem:
"A convex spherical mirror is 25 ft from the door of a convenience store. The clerk needs to see a 6 ft. person entering the store at least 3 inches tall in the mirror to identify them. What is the radius of the mirror?"
d_obj = do = 25 ft = 300 inches
h_img = hi = 3 inches
h_obj = ho = 6 ft = 72 inches
The formulas I tried using:
focal point = f = radius/2 = r/2
1/do+1/di = 1/f = 1/r/2 = 2/r
For convex mirror: m = magnification = hi/ho = -di/do
Work:
hi/ho = -di/do
3/72 = -di/300
di=-12.5 inches
1/do + 1/di = 2/r
1/300 - 1/12.5 = 2/r
r=26 inches
I found the radius to be 26 inches, which seems a bit too large. Is it correct or am I doing something wrong? I feel as though I must somehow incorporate the magnification, but I'm not sure how. It would be -24X but looking at something normally you'll see it as smaller than it is if you're at a greater distance so I'm not sure how to compensate for that.
"A convex spherical mirror is 25 ft from the door of a convenience store. The clerk needs to see a 6 ft. person entering the store at least 3 inches tall in the mirror to identify them. What is the radius of the mirror?"
d_obj = do = 25 ft = 300 inches
h_img = hi = 3 inches
h_obj = ho = 6 ft = 72 inches
The formulas I tried using:
focal point = f = radius/2 = r/2
1/do+1/di = 1/f = 1/r/2 = 2/r
For convex mirror: m = magnification = hi/ho = -di/do
Work:
hi/ho = -di/do
3/72 = -di/300
di=-12.5 inches
1/do + 1/di = 2/r
1/300 - 1/12.5 = 2/r
r=26 inches
I found the radius to be 26 inches, which seems a bit too large. Is it correct or am I doing something wrong? I feel as though I must somehow incorporate the magnification, but I'm not sure how. It would be -24X but looking at something normally you'll see it as smaller than it is if you're at a greater distance so I'm not sure how to compensate for that.