Calculating Image Height and Distance

The size of the image focused on the retina and the distance between the lens and the retina can be calculated using two mathematical equations: the lens equation and the magnification equation.

Sample problem: Calculate the image height and distance when focusing on a tree that is 5 m tall and 10 m away from you. Assume that your focal point is 0.0180 m.

Given: h(object) = 5 m, d(object) = 10 m, f = 0.0180 m

Use the lens equation to find the image distance:

1/f = 1/d(object) + 1/d(image)

d(image) = 1/[1/f -1/d(object)

=1/[(1/0.0180 m) - (1/10m)]

d(image) = 0.0180 m

Use the magnification equation to find the image height:

h(image)/h(object) = -d(image)/d(object)

h(image) = -d(image)/d(object) * h(object)

= -0.0180 m/10 m(5 m)

h(image) = -0.0812 m

According to these calculations, the image on the retina is 1.80 cm from the lens. The image is 8.12 cm tall. The negative sign shows that the image on the retina is upside down from the object in real life.

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