Violet light and red light travel through air and strike a block of plastic at the same angle of incidence. The angle of refraction is 30.700° for the violet light and 31.380° for the red light. The index of refraction for violet light in plastic is greater than that for red light by 0.0420. Delaying any rounding off of calculations until the very end, find the index of refraction for violet light in plastic.

sin i / sin 31.380 = sin i / sin 30.700 - 0.0420

Can you help me solve?

sin i / sin 31.380 = nv-.0420

sin i/(sin 30.7)=nv

sini=(nv-.0420)*sin31.389
sini=nv* sin30.7
set them equal, solve for nv

To find the index of refraction for violet light in plastic, you can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction for the two mediums (air and plastic).

The equation you have written is correct:
sin i / sin 31.380 = sin i / sin 30.700 - 0.0420

To solve for the index of refraction for violet light in plastic, follow these steps:

1. Rearrange the equation to isolate the terms that involve the index of refraction for violet light in plastic.

sin i / sin 31.380 = sin i / (sin 30.700 - 0.0420)

2. Cross multiply the equation to remove the fractions.

sin i * (sin 30.700 - 0.0420) = sin i * sin 31.380

3. Expand the equation by multiplying the terms.

sin i * sin 30.700 - sin i * 0.0420 = sin i * sin 31.380

4. Distribute the sin i term on the left side of the equation.

sin i * sin 30.700 - 0.0420 * sin i = sin i * sin 31.380

5. Combine like terms on the left side of the equation.

sin i * (sin 30.700 - 0.0420) = sin i * sin 31.380

6. Divide both sides of the equation by sin i.

sin 30.700 - 0.0420 = sin 31.380

7. Use a scientific calculator to evaluate the right side of the equation.

sin 30.700 - 0.0420 = 0.5138

8. Add 0.0420 to both sides of the equation.

sin 30.700 = 0.5138 + 0.0420

9. Use a scientific calculator to evaluate the right side of the equation.

sin 30.700 = 0.5558

10. Divide both sides of the equation by 0.5558.

sin 30.700 / 0.5558 = 1

11. Use a scientific calculator to evaluate the left side of the equation.

0.5539 / 0.5558 = 0.9930

The index of refraction for violet light in plastic is approximately 0.9930.

Certainly! Let's solve the equation to find the index of refraction for violet light in plastic. Here's how to do it step by step:

1. Start with the given equation: sin(i) / sin(31.380°) = sin(i) / (sin(30.700°) - 0.0420).

2. Multiply both sides of the equation by sin(31.380°) to eliminate the fraction on the left side: sin(i) = (sin(i) / (sin(30.700°) - 0.0420)) * sin(31.380°).

3. Distribute sin(31.380°) to the right side of the equation: sin(i) = (sin(31.380°) * sin(i)) / (sin(30.700°) - 0.0420).

4. Multiply both sides of the equation by (sin(30.700°) - 0.0420) to get rid of the fraction on the right side: (sin(30.700°) - 0.0420) * sin(i) = sin(31.380°) * sin(i).

5. Expand the left side of the equation: sin(30.700°) * sin(i) - 0.0420 * sin(i) = sin(31.380°) * sin(i).

6. Subtract sin(i) from both sides of the equation: sin(30.700°) * sin(i) - 0.0420 * sin(i) - sin(i) = sin(31.380°) * sin(i) - sin(i).

7. Combine like terms: sin(30.700°) * sin(i) - (0.0420 + 1) * sin(i) = sin(31.380°) * sin(i) - sin(i).

8. Simplify and isolate sin(i) on one side of the equation: [sin(30.700°) - (0.0420 + 1)] * sin(i) = (sin(31.380°) - 1) * sin(i).

9. Divide both sides of the equation by [(sin(30.700°) - (0.0420 + 1)] to solve for sin(i):
sin(i) = (sin(31.380°) - 1) / [sin(30.700°) - (0.0420 + 1)].

10. Use the inverse sine function on both sides to find the angle i: i = arcsin[(sin(31.380°) - 1) / [sin(30.700°) - (0.0420 + 1)]].

11. Finally, calculate the index of refraction for violet light in plastic using the relationship between the angle of incidence and the index of refraction: index of refraction = sin(30.700°) / sin(i), where i is the angle found in step 10.

By plugging in the values from the problem into the equation and performing the calculations, you should be able to find the index of refraction for violet light in plastic.