Determination of the wavelength of a spectral line

[mstud]

Homework Statement

With a spectrometer we can see a black line in the spectrum of the sun at the angle $$\theta =20,73$$ from the maxima of 0. order. The line is in the maxima of the second order. Use the interference formula (given under heading 2) to determine the wavelength and color this line equals to. The used lattice has 300 lines / mm, that is d= 1mm/300.

Homework Equations

$$dsin\theta =n\lambda$$ d is the distance between the lines in the lattice used,theta the angle from the zero-th maxima and n the order of the maxima in which the line is.

The Attempt at a Solution

$$\lambda=\frac{\frac {1 \cdot 10^{-3} m}{300} \cdot sin (20,73)}{2}\approx 1,590 \cdot 10^{-6} m = 1590 nm$$

The answer key of my book says 590 nm. And my answer even says that the radiation is infrared, so I must be wrong :-(

Does anybody see what's gone wrong here ? Thanks.

 

[phyzguy]

You probably have your calculator in radians, and the given angle is 20.73 degrees. Always check.

 

[mstud]

That was the case. Haven't used my calculator for calculation of angles since I worked with radians in mathematics this spring...

Thank you for your help :D