In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when another light source of wavelength $$\lambda$$ is used. Then the value of $$\lambda$$ is (in nm) ___________.

Fringe width definition: $$\beta = \frac{\lambda D}{d}$$

Total linear width of a section containing $$n$$ fringes: $$\Delta x = n\beta = \frac{n\lambda D}{d}$$

Since the section width $$\Delta x$$, slit distance $$d$$, and screen distance $$D$$ remain constant:

$$n_1 \lambda_1 = n_2 \lambda_2$$

$$15 \times 500 = 10 \times \lambda_2$$

$$\lambda_2 = \frac{7500}{10} = 750\text{ nm}$$