- #1

unscientific

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## Homework Statement

Light from infinity strikes a diffracting grating normally with 600 lines per mm. The emitted light then passes through a lens to project visible light (400-800 nm) spectrum onto a screen that is 50mm, just enough to cover it. Find the focal length of the lens.

## Homework Equations

## The Attempt at a Solution

Lens maker's Equation:

[tex]1/u + 1/v = 1/f[/tex]

Let u -> ∞,

Thus ##v = f##, so the emitted light is focused on the paper.

[tex]d sin \theta = n\lambda[/tex]

I can't find a way to solve this question unless ##n## is known...I shall let n = 1.

[tex]\frac{y}{\sqrt{y^2 + f^2}}[/tex] = \lambda [/tex]

Solving,

[tex] f = 22.4 m[/tex]

This is a strange setup, imagine the photographic paper would have to be placed so far away from the lens! (Relative to its size)