3. D9: I can compute derivatives of implicitly defined functions. D10: I can find the equation of the line tangent to a function at a point and use this line as a linear approximation to estimate the value of a function at nearby points. nteds Snell's Law or the Law of Refraction describes the behavior of light as it travels between two substances, telling us how light bends. Snell's law tells us about the relationship be- tween the angle of incidence, 01, and the angle of refraction, 02, as a ray of light travels from one medium to another and depends on the refrac- tion indices n₁ and n₂ of both of the substance. Snell's Law n₁ sin(01) = n2 sin (02) (a) Which letters represent variables? Air (1) 01 02 Glass (n2) (b) Which letters represent constants? d02 (c) (D9) Use Implicit differentiation to compute d01 (d) The refraction index of air is n₁ = 1 and the refraction index of glass is n2 = 1.52. If the angle of incidence is 0₁ = 20° verify that the angle of refraction is approximately 02 ≈ 13°. (Make sure you calculator is in degrees mode, and just plug in numbers to verify the equation balances.) (e) (D10) Find an equation for the tangent line when 0₁ = 20° and 62 = 13° (f) (D10) Use your tangent line to approximate the value of 02 when ₁ = 21°
3. D9: I can compute derivatives of implicitly defined functions. D10: I can find the equation of the line tangent to a function at a point and use this line as a linear approximation to estimate the value of a function at nearby points. nteds Snell's Law or the Law of Refraction describes the behavior of light as it travels between two substances, telling us how light bends. Snell's law tells us about the relationship be- tween the angle of incidence, 01, and the angle of refraction, 02, as a ray of light travels from one medium to another and depends on the refrac- tion indices n₁ and n₂ of both of the substance. Snell's Law n₁ sin(01) = n2 sin (02) (a) Which letters represent variables? Air (1) 01 02 Glass (n2) (b) Which letters represent constants? d02 (c) (D9) Use Implicit differentiation to compute d01 (d) The refraction index of air is n₁ = 1 and the refraction index of glass is n2 = 1.52. If the angle of incidence is 0₁ = 20° verify that the angle of refraction is approximately 02 ≈ 13°. (Make sure you calculator is in degrees mode, and just plug in numbers to verify the equation balances.) (e) (D10) Find an equation for the tangent line when 0₁ = 20° and 62 = 13° (f) (D10) Use your tangent line to approximate the value of 02 when ₁ = 21°
University Physics Volume 3
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Chapter4: Diffraction
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it is not graded!! the d9 and d10 are just standards!!
Transcribed Image Text:3. D9: I can compute derivatives of implicitly defined functions.
D10: I can find the equation of the line tangent to a function at a point and use this line as a
linear approximation to estimate the value of a function at nearby points.
nteds
Snell's Law or the Law of Refraction describes the behavior of light as it travels between two
substances, telling us how light bends.
Snell's law tells us about the relationship be-
tween the angle of incidence, 01, and the angle
of refraction, 02, as a ray of light travels from one
medium to another and depends on the refrac-
tion indices n₁ and n₂ of both of the substance.
Snell's Law
n₁ sin(01) = n2 sin (02)
(a) Which letters represent variables?
Air (1)
01
02
Glass (n2)
(b) Which letters represent constants?
d02
(c) (D9) Use Implicit differentiation to compute
d01
(d) The refraction index of air is n₁ = 1 and the refraction index of glass is n2 = 1.52. If the
angle of incidence is 0₁ = 20° verify that the angle of refraction is approximately 02 ≈ 13°.
(Make sure you calculator is in degrees mode, and just plug in numbers to verify the equation
balances.)
(e) (D10) Find an equation for the tangent line when 0₁ = 20° and 62 = 13°
(f) (D10) Use your tangent line to approximate the value of 02 when ₁ = 21°
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9781938168185
Author:
William Moebs, Jeff Sanny
Publisher:
OpenStax