Radius of convex spherical mirror?

[gmmstr827]

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.

 

[ehild]

The image is real and upside down, so the height of the image is negative. Therefore, di is positive.

ehild

Edit: I was wrong: The mirror is convex, so the image is upright (virtual). Di is positive!

 

[gmmstr827]

The image is real and upside down, so the height of the image is negative. Therefore, di is positive.

ehild

d_obj = do = 25 ft = 300 inches
h_img = hi = -3 inches
h_obj = ho = 6 ft = 72 inches

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=24 inches

So the radius of the mirror is precisely 24 inches? That still seems like a rather large convenience store mirror.

 

[ehild]

It is the radius of the curvature. A spherical mirror is a part of a spherical surface, its diameter can be as small as you like.

ehild

 

[gmmstr827]

Okay, thank you!

 

[ehild]

Sorry I was wrong, mixed convex and concave. The clerk does not want to see people upside down! He/she uses a convex mirror, that produces virtual, upright image. For such an image, di is positive, but the focal distance is negative. From the mirror equation, you get f=-13 inch. So the 26 inch for the radius was correct.

ehild

 

[gmmstr827]

Okay, thanks. I was wondering about the inverted image, though the result seemed better.