Question

A camera with a 100 mm-focal length lens is used to photograph the sun. What is the height of the image of the sun on the film, given the sun is 1.40×10⁶km in diameter and is 1.50×10⁸km away?

Answer 1

The height of the image of the sun on the film is approximately 1.12 mm.

Step-by-step explanation:

To determine the height of the image of the sun on the film, we can use the magnification formula:

`\[ \text{Magnification} = -\frac{\text{Image Height}}{\text{Object Height}} \]`

Given that the focal length of the lens
`(\( f \))` is 100 mm and the object distance
`(\( u \))` is the distance to the sun (1.50×10⁸ km), we can use the lens formula:

`\[ (1)/(f) = (1)/(u) + (1)/(v) \]`

Rearranging the formula to solve for
`\( v \)` (image distance), we find:

`\[ v = (fu)/(f-u) \]`

Now, we can use the magnification formula to find the image height:

`\[ \text{Magnification} = (v)/(u) \]`

Substituting the values we obtained earlier:

`\[ \text{Magnification} = -(fu)/(f(f-u)) \]`

With the magnification given as -1, representing an inverted image, we can rearrange the formula to solve for the image height:

`\[ \text{Image Height} = (fu)/(f-u) \]`

Plugging in the values, we get:

`\[ \text{Image Height} \approx 1.12 \, \text{mm} \]`

Therefore, the height of the image of the sun on the film is approximately 1.12 mm.