Calculating Image Distance Using a Christmas Tree Ball

[Jess_18033152]

Homework Statement

You look at yourself in a shiny Christmas tree ball, which has a diameter of 9.63 cm. If your face is 7.81 cm away from the shiny ball, calculate the image distance.

Homework Equations

?
Thinking I would use
magnification = di/d0

di = 0.0781m
d0 = 0.0963m

The Attempt at a Solution

-0.811m

This doesn't sound right to me, is this perhaps because di is supposed to be what I'm trying to find out?

If so, would I then assume that the magnification is 0.0781 and I need to times that by 0.0963 to work out di? The the calculations would be as follows;?

m x do = di

di = 0.0781 x 0.0963
= 7.52 x 10^-3 m (3sf)

I think this would be the correct way to work out this question, I just wanted to double check that my second method is correct?

 

[Wrichik Basu]

I don't think magnification formulae will help you here. You're given the object distance and a ball, which acts like a convex mirror. Have you tried using the mirror formula $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$ with the proper signs?

What answer is supplied with the book?

 

[Drakkith]

This doesn't sound right to me, is this perhaps because di is supposed to be what I'm trying to find out?

That's right. You have dO, the distance from the object to the mirror, and you're asked to find dI, the image distance.

If so, would I then assume that the magnification is 0.0781 and I need to times that by 0.0963 to work out di? The the calculations would be as follows;?

No, you don't immediately have the magnification because you don't have the image distance.

Look at the information provided to you. You have dO and the diameter of the mirror. For an optical surface we usually work with the radius of curvature $R$, not the diameter. Find $R$ and see if you have any equations that you can use $R$ into get the image distance or another helpful property.