The index of refraction for a diamond for red light of wavelength 660 nm is 2.35

Question

The index of refraction for a diamond for red light of wavelength 660 nm is 2.35, while that for blue light of wavelength 437 nm is 2.26. Suppose white light Ls incident on the diamond at 33.8 degree . Find the angle of refraction for red light. Answer in units of degree Find the angle of refraction for blue light. Answer in units of degree An cylindrical opaque drinking glass has a diameter 3.6 cm and height h. as shown in the figure. An observer's eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled to the brim with a transparent liquid, the observer can just barely see the center of the bottom of the glass. The liquid in the drinking glass has an index of refraction of 1.24 . Calculate the height h of the glass. Answer in units of cm The index of refraction for violet light in silica flint glass is 1.66. and that for red light is 1.61. What is the angle of deviation for the red ray passing through a prism of apex angle 59.5 degree if the angle of incidence is 43.6 degree ? Answer in units of degree What Ls the angular dispersion of visible light with the same angle of incidence? The critical angle for a special type of glass in air is 30 degree . The index of refraction for water is 1.33. What is the critical angle if the glass is immersed in water? A concave mirror has a radius of curvature of 1.6 m. Calculate the position of the image produced when an object is placed 2.19 m from the mirror. Calculate the position of the image when an object is placed 0.501 m from the mirror.

Explanation / Answer

1) for red light sin(i)/sin(r) = 2.35

==> sin(r) = sin(33.8 degree)/2.35 = 0.23

==> r = arcsin(0.23) = 13.6 degree

for blue light

r = arcisn(sin(33.8 degree)/2.26) = 14.2 degree

2) tan(thetar) = d/h

tan(thetai) = d/2h

sin(thetar)/sin(thetai) = 1.24

==> d/sqrt(d^2+h^2)/d/sqrt(d^2+4h^2) = 1.24

==> d^2+4h^2/(d^2+h^2) = 1.24^2 = 1.536

==> d^2+4h^2 = 1.536d^2+1.536h^2

==> 2.4624h^2 = 0.536d^2

==> h = d*sqrt(0.536/2.4624) = 3.6*sqrt(0.536/2.4624) = 1.7 cm

thetar =arctan(d/h) = arctan(3.6/1.7) = 64.7 degree

thetar = 64.7 degree

h = 1.7 cm

3) n = sin((A+D)/2)/sin(A/2)

wher n is refractive index A is abgle of prism or apex angle and D is angle of deviation

2*arcsin(1.61*sin(59.5 degree)) = 59.5+D

==> D = 106.05 -59.5 = 46.5 degree

for violet

D = 51.4 degree

so angular depression = 51.4-46.5 = 4.9 degree

4)sin(i)/sin(r) = 1/n

here r = 90 and i = 30

so n = 1/sin(30) = 2

now when in water

sin(i) = 1.33/2

==> i = arcsin(0.665) = 41.6 degree

1/v+1/u = 1/f

==> 1/v -1/2.19 = -2/1.6

==> 1/v = 1/2.19-1/0.8 = -0.79

==> v = -1.26 m

so v = 1.26 m on the same side as that of object

1/v = 1/0.501-1/0.8 = 0.74

==> v = 1.34 m

so v = 1.34 image is virtual

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