10 pts: Physics 101 Light/Waves HW

Question

I) Find the wavelength of light in the following scenario: Monochromatic light hits two slits 0.5 mm apart. Successive nodal points on a screen 4 m away are 4.5 cm apart close to the center of the pattern.

II) Find the separation between 2 slits where 700 nm orange light has its first max. at a angle of 5 degrees

III) A beam with a wavelength of 500nm falls on one slit producing a central maximum 4.5 cm wide on a screen 1.5 m away. Find the slit width.

Thanks in advance for your help =)

Answer 1

I can never remember the damned formula, but deriving it is easy.  Draw a triangle, using the two slits and the first node.  Drop a perpendicular from the upper slit point to the lower leg of the triangle.  The little triangle made by this perpendicular, the slit spacing, and the small distance on the line from the bottom slit is similar to the triangle you first drew.  Now the small distance referred to above is one wavelength, so you can do a bit of algebra and solve the whole thing.