- #1

harrypoterfan

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- Homework Statement
- A convex mirror with a radius of curvature of −30.0 cm is used to form an image of an arrow that is 10.6 cm away from the mirror. If the arrow is 1.70 cm tall and inverted (pointing below the optical axis), what is the height of the arrow's image? (Include the sign of the value in your answer.)

- Relevant Equations
- $$f = -\frac{1}{r}$$

$$f^-1 = d_i^{-1} + d_0^{{-1}$$

$$m = \frac{h_i}{h_0} =-\frac{d_i}/{d_o}$$

$$f = -\frac{-30}{2} = 15$$

solving for ##d_0## in $$f^{-1} = d_i^{-1} + d_0^{-1}$$,

$$d_0 = (f^{-1} - d_i^{-1})^{-1}$$

= -36.1364

solving for ##h_i## in $$m = \frac{h_i}{h_0} =-\frac{d_i}{d_o}$$,

$$h_i = -d_i\times\frac{h_0}{d_o} = 0.4987$$

I'm told by webassign that it should be negative and that -0.4987 is off by more than 10%

solving for ##d_0## in $$f^{-1} = d_i^{-1} + d_0^{-1}$$,

$$d_0 = (f^{-1} - d_i^{-1})^{-1}$$

= -36.1364

solving for ##h_i## in $$m = \frac{h_i}{h_0} =-\frac{d_i}{d_o}$$,

$$h_i = -d_i\times\frac{h_0}{d_o} = 0.4987$$

I'm told by webassign that it should be negative and that -0.4987 is off by more than 10%