A diamond's index of refraction for red light, 656 nm is 2.410 while that for blue light, 434 nm, is 2.450. Suppose white light is incident on the diamond at 30 degrees. Find the angles of refraction for these two colors.
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working out those question for me please help me.
Well, it seems like this diamond is feeling a bit indecisive with its refraction angles! Let's see if we can figure it out.
First, we can use Snell's Law to solve for the angles of refraction. Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction:
n1 * sin(theta1) = n2 * sin(theta2)
For red light:
n1 = 2.410 and n2 = 1 (since red light is passing from a higher index medium, the diamond, to a lower index medium, the air).
So, we have:
2.410 * sin(30 degrees) = 1 * sin(theta2_red)
Now, let's calculate:
sin(theta2_red) = (2.410 * sin(30 degrees)) / 1
theta2_red = arcsin((2.410 * sin(30 degrees)) / 1)
Phew, that's a mouthful! Let me grab my calculator to figure this out for you.
Calculating...calculating...
Okay, after some quick calculations, the angle of refraction for red light is approximately 19.19 degrees.
Now, let's move on to blue light!
For blue light:
n1 = 2.450 and n2 = 1 (since blue light is passing from a higher index medium, the diamond, to a lower index medium, the air).
Using Snell's Law again, we have:
2.450 * sin(30 degrees) = 1 * sin(theta2_blue)
Now, time for another calculation:
sin(theta2_blue) = (2.450 * sin(30 degrees)) / 1
theta2_blue = arcsin((2.450 * sin(30 degrees)) / 1)
Getting my calculator back out...calculating... !
Alright, the angle of refraction for blue light is approximately 19.64 degrees.
So, there you have it! The angles of refraction for red light and blue light are approximately 19.19 degrees and 19.64 degrees, respectively. Looks like the diamond is making up its mind, one refraction angle at a time!
To find the angles of refraction for red and blue light incident on a diamond, we can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction of the two media.
Let's denote the angle of incidence as θ and the angle of refraction as θ'.
For red light (656 nm), the index of refraction is 2.410. We can use the equation sin(θ)/sin(θ') = 2.410.
For blue light (434 nm), the index of refraction is 2.450. We can use the equation sin(θ)/sin(θ') = 2.450.
Next, we can determine the critical angle for total internal reflection for each wavelength of light. The critical angle is the angle of incidence where the angle of refraction becomes 90 degrees.
For red light, we have sin(θ_c) = 1/2.410 = 0.4149, which means θ_c ≈ 24.0 degrees.
For blue light, we have sin(θ_c) = 1/2.450 = 0.4082, which means θ_c ≈ 24.8 degrees.
Since the angle of incidence is given as 30 degrees, which is greater than both critical angles, there will be no total internal reflection.
Finally, to find the angles of refraction, we can solve the Snell's Law equations for θ':
For red light: sin(30)/sin(θ') = 2.410. Rearranging the equation, we get sin(θ') = sin(30)/2.410. Taking the inverse sine, we find θ' ≈ 12.3 degrees.
For blue light: sin(30)/sin(θ') = 2.450. Rearranging the equation, we get sin(θ') = sin(30)/2.450. Taking the inverse sine, we find θ' ≈ 12.1 degrees.
Therefore, the angles of refraction for red and blue light incident on the diamond at 30 degrees are approximately 12.3 degrees and 12.1 degrees, respectively.
Use Snell's Law: n1sin(theta1)=n2sin(theta2)
Since white light is incident at 30degrees, theta1 = 30.
Calculate the angle of refraction for the blue and red lights separately. For each case, n1 should be the index of air while n2 is the index for the blue or red light of diamond.