Refraction, how tall is the image?

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AI Thread Summary
To find the height of the image (Hi) given the object height (Ho) of 0.5 m, object distance (So) of 2.0 m, and image distance (Si) of 8.0 m, the equation Ho / Hi = So / -Si is used. The user is confused about isolating Hi in the equation. The solution involves cross-multiplying to eliminate fractions, leading to the equation 0.5 * 8.0 = 2.0 * Hi. This simplifies to Hi = (0.5 * 8.0) / 2.0, allowing for the calculation of the image height. The discussion emphasizes the importance of correctly manipulating equations to solve for unknown variables.
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Homework Statement



If the object distance in the following picture were 8.0 m and the image distance were 2.0 m, and the object is 0.50 m tall, how tall is the image.

Ho = 0.5
So = 2.0
Si = 8.0

Homework Equations


Ho / Hi = So / -Si
In order these variables are hight object, hight image, object distance and object image.

The Attempt at a Solution



0.5/ Hi = 2.0/8.0

This is where the problem occurs. How do I get Hi on one side of the equation?

I don't know how to move the numerator to the other side of the equation... Please help... I think there is a very simple solution but, it is eluding me.
 
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Where did the minus sign go?
Cross multiply to eliminate all fractions:
0.5*8.0 = 2.0*Hi
 

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