Solving for image height given ##h_o, d_i##, and r

In summary, the conversation involves solving for ##d_0## and ##h_i## in two equations, with a given focal length of a convex mirror. The solution for ##d_0## is -36.1364, and the solution for ##h_i## is 0.4987. The sign conventions for mirrors should be followed, with the focal length being negative for a convex mirror.
  • #1
harrypoterfan
1
0
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%

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.)
 
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  • #2
Be sure you are following the sign conventions that are used in your course for mirrors. Usually, the conventions are such that the focal length of a convex mirror is negative.

You solved for ##d_0##. But ##d_0## is given. You need to find ##d_i##.
 
Last edited:

Related to Solving for image height given ##h_o, d_i##, and r

What are the variables in the equation for solving for image height given the object height, distance to the image, and radius?

The variables in this equation are the object height (ho), distance to the image (di), and radius (r).

What is the formula for solving for image height given the object height, distance to the image, and radius?

The formula for solving for image height is hi = ho * (di / r).

How do you determine the units of measurement for the image height?

The units of measurement for the image height will be the same as the units of measurement for the object height and distance to the image. It is important to ensure that all units are consistent in order to get an accurate result.

Can the equation for solving image height be used for any shape of lens or mirror?

Yes, the equation can be used for any shape of lens or mirror as long as the distance to the image and radius are measured from the center of the lens or mirror.

What are some real-world applications of solving for image height?

Solving for image height is important in various fields such as photography, optics, and engineering. It can be used to determine the size and position of an image formed by a lens or mirror, which is crucial in designing and creating optical instruments. It is also used in calculating magnification and resolving power in photography and microscopy.

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