It is possible to measure tryptophan fluorescence with the Vernier Fluorescence/UV-VIS Spectrophotometer. Here are some tips to help you:

1. You will need to purchase the 280 nm LED separately.
2. To avoid the inner filter effect, you will need a solution of pH 7 tryptophan that has an absorbance value of less that 1.0. The data shown below was taken with 1.2e-4 M trp in 0.1 M pH 7 phosphate buffer.
3. You will need to adjust the collection settings in the spectrometer settings box. Feel free to play with these settings to see how they affect your data’s presentation. A great overview of them is available here. You can see the sample data settings in the screenshot below.
4. Tryptophan solutions degrade very quickly. Be prepared to make these solutions fresh on the day of measurement.

Also see
Fluorescence/UV-VIS Spectrophotometer Troubleshooting and FAQs
What are some tips for improving my Fluorescence/UV-VIS Spectrophotometer data?