The interference patterns produced by a diffraction grating and by a double slit are compared. With the diffraction grating, yellow light in the first order is observed at $30^{\circ}$ to the normal of the grating. The same light forms interference fringes on a screen $1.0\,\text{m}$ away from the double slit. The slit separation is $500$ times larger than the line spacing of the grating. What is the fringe separation on the screen?
- A$2.5 \times 10^{-7}\,\text{m}$
- B$1.0 \times 10^{-5}\,\text{m}$
- C$1.0 \times 10^{-3}\,\text{m}$
- D$1.0 \times 10^{-1}\,\text{m}$