Refraction, how tall is the image?

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SUMMARY

The discussion focuses on calculating the height of an image (Hi) using the formula Ho / Hi = So / -Si, where Ho represents the height of the object, So is the object distance, and Si is the image distance. Given that Ho is 0.5 m, So is 2.0 m, and Si is 8.0 m, the user struggles with isolating Hi in the equation. The correct approach involves cross-multiplying to eliminate fractions, leading to the equation 0.5 * 8.0 = 2.0 * Hi, which allows for straightforward calculation of Hi.

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  • Familiarity with the thin lens formula and magnification equations.
  • Ability to manipulate algebraic equations for solving variables.
  • Knowledge of cross-multiplication in fractions.
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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 height object, height 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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