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Math 20 - Calculus I $4.2 - Extra Credit Applied Project: The Calculus of Rainbows Show...
Rainbows are created when sunlight of different wavelengths (colors) is refracted and reflected in raindrops. The angle of elevation θ of a rainbow is always the same. It can be shown that θ = 4β-. 2a, where k sin(β) sin(a) and α 59.4° and k 1.33 is the index of refraction of water. Use the given information to find the angle of elevation θ of a rainbow. Hint: Find sin A]+ (Round your answer to one decimal place.) then use...
Problem 2 Show that for an index ofrefraction k that D(a) is minimized when sin α- 4 Use this to obtain p- arcsin to obtain ß arcsinand fil in the following table. 4-k2 3k2 a in degrees B in degrees R(a) in degrees Color Red Orange Yellow Green Bluc Indigo Violet 1.331 1.332 1.333 1.335 1337 1.340 1.344 The values of R(a) you obtained in the table accounts for the various color bands that appear in the rainbow as sunlight...
Sunlight strikes a piece of crown glass at an angle of incidence of 39.4o. Calculate the difference in the angle of refraction between a red (660 nm) and a violet (410 nm) ray within the glass. The index of refraction is n=1.520 for red and n=1.538 for violet light. Tries 0/20 The ray now travels inside the glass. What is the minimum angle of incidence at which the red ray can hit the surface of the glass and become there...
part f and g i cant figure out Question 3 1 pts Silica flint a Problem The index of refraction for red light in silica flint glass is 1.62, and for violet light is 1.66. If red light is incident on the left side of a triangular at 01 = 60 degrees, what is the refracted angle 02 (in degrees)? The glass is surrounded by air on all sides. Deviation angle for red light 40° Question 4 1 pts Silica...
Sunlight strikes a piece of crown glass at an angle of incidence of 30.2degree. Calculate the difference in the angle of refraction between a red (660 nm) and a blue (470 nm) ray within the glass. The index of refraction is n=1.520 for red and n = 1.531 for blue light. Submit Answer Tries 0/15 The ray now travels inside the glass. What is the minimum angle of incidence at which the red ray can hit the surface of the...
In a diamond, the index of refraction for violet light (λ = 400 nm) is 2.46, and for red light (λ = 700 nm) it is 2.41. A ray of light traveling through air strikes the diamond surface at an angle of 42.8° to the normal. What is the angular separation between these two colors of light in the refracted ray? A. 0.72° B. 0.35° C. 0.96° D. 1.16°
A beam of white light is incident on the surface of a diamond at an angle θa. (Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. For example, the indices of refraction in diamond are nred=2.410 for red light and nblue=2.450 for blue light. Thus, blue light and red light are refracted at different angles inside the diamond, as shown in...
water interface (the surface of the lake), it is partly reflected back into the air and partly refracted or transmitted into the water. This explains why on the surface of a lake sometimes you see the reflection of the surrounding landscape and other times the underwater vegetation. These effects on light propagation occur because light travels at different speeds depending on the medium. The index of refraction of a material, denoted by n, gives an indication of the speed of...
1) In a ruby laser, light is produced in a solid rod of ruby, with refractive index 1.77. The light emerges from the end of the rod into the surrounding air. Part A At what angle should the rod end be cut so the emerging light is fully polarized? 2) A beam of white light is incident on the surface of a diamond at an angle θa. (Figure 1) Since the index of refraction depends on the light's wavelength, the...
10.A narrow beam of white light is incident normally on the surface of a triangular silicate flint glass prism with one angle of 90. The index of refraction for violet light is 1.66 and for red light is 1.61. The angle in the prism is equal to 30° of glass. a. On the diagram below show an approximate sketch for the refracted light from the opposite face of the prism. Air B White light 780° Glass Calculate angular separation between...