2. The Impressionist painter Georges Seurat created paintings with an enormous n

Question

2. The Impressionist painter Georges Seurat created paintings with an enormous number of dots of pure pigment, each of which was approximately 2.00 mm in diameter. The idea was to have colors such as red and green next to each other to form a scintillating canvas. Outside what distance would one be unable to discern individual dots on the canvas? (Assume that ? = 500 nm and that the pupil diameter is 4.00 mm.)

3. A piece of transparent material having an index of refraction n is cut into the shape of a wedge as shown . The angle of thewedgeissmall.Monochromaticlightofwavelength ?is normally incident from above, and viewed from above. Let h represent the height of the wedge and l its width.Show that bright fringes occur at the positions

x = ?l(m + 1?2)/2hn and dark fringes occur at the positions x = ?lm/2hn, where m = 0, 1, 2, . . . and x is measured as shown.

Explanation / Answer

Wavelength ? = 500 * 10 ^ -9 m

Pupil diameter d= 4 * 10 ^-3 m

Diameter of pigment x = 2 * 10 ^ -3 m

We know x = 1.22 ?D / d

From this required distance D = xd / 1.22?

= 13.12 m

3)

Bright fringes when 2t = lambda/n (m +1/2)

Dark fringes when 2t = ( lambda/n )m

But tan q = h/l

(slope) => t(x)=(h/l)x

Insert t into the equations above and solve for x ,

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