Calculate the speed of light for the following mediums

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Calculate the speed of light for the following mediums: Water (n=1.33); b. Diamond (n=2.42) Plexiglas (n=1.51) Calculate the refractive index for a substance if the speed of light in that medium is 2.1x 108 m/s b. 1.5X 108 mls 3. Calculate the speed of light in a hypothetical material you have discovered, its refractive index is 0.90

The Correct Answer and Explanation is:

Part 1: Calculating the Speed of Light in Different Mediums

The speed of light in a given medium can be calculated using the formula:v=cnv = \frac{c}{n}v=nc​

Where:

  • vvv is the speed of light in the medium (m/s),
  • ccc is the speed of light in a vacuum (approximately 3.00×1083.00 \times 10^83.00×108 m/s),
  • nnn is the refractive index of the medium.

Let’s calculate the speed of light in each medium:

a. Water (n = 1.33)v=3.00×108 m/s1.33=2.26×108 m/sv = \frac{3.00 \times 10^8 \, \text{m/s}}{1.33} = 2.26 \times 10^8 \, \text{m/s}v=1.333.00×108m/s​=2.26×108m/s

So, the speed of light in water is approximately 2.26×1082.26 \times 10^82.26×108 m/s.

b. Diamond (n = 2.42)v=3.00×108 m/s2.42=1.24×108 m/sv = \frac{3.00 \times 10^8 \, \text{m/s}}{2.42} = 1.24 \times 10^8 \, \text{m/s}v=2.423.00×108m/s​=1.24×108m/s

The speed of light in diamond is approximately 1.24×1081.24 \times 10^81.24×108 m/s.

c. Plexiglas (n = 1.51)v=3.00×108 m/s1.51=1.99×108 m/sv = \frac{3.00 \times 10^8 \, \text{m/s}}{1.51} = 1.99 \times 10^8 \, \text{m/s}v=1.513.00×108m/s​=1.99×108m/s

So, the speed of light in Plexiglas is approximately 1.99×1081.99 \times 10^81.99×108 m/s.

Part 2: Calculating the Refractive Index for a Substance

The refractive index nnn can be calculated using the formula:n=cvn = \frac{c}{v}n=vc​

Where:

  • nnn is the refractive index,
  • ccc is the speed of light in a vacuum (approximately 3.00×1083.00 \times 10^83.00×108 m/s),
  • vvv is the speed of light in the medium (m/s).

a. Given the speed of light as 2.1×1082.1 \times 10^82.1×108 m/s:n=3.00×108 m/s2.1×108 m/s=1.43n = \frac{3.00 \times 10^8 \, \text{m/s}}{2.1 \times 10^8 \, \text{m/s}} = 1.43n=2.1×108m/s3.00×108m/s​=1.43

The refractive index of the substance is n=1.43n = 1.43n=1.43.

b. Given the speed of light as 1.5×1081.5 \times 10^81.5×108 m/s:n=3.00×108 m/s1.5×108 m/s=2.00n = \frac{3.00 \times 10^8 \, \text{m/s}}{1.5 \times 10^8 \, \text{m/s}} = 2.00n=1.5×108m/s3.00×108m/s​=2.00

The refractive index of the substance is n=2.00n = 2.00n=2.00.

Part 3: Speed of Light in a Hypothetical Material

If you have discovered a material with a refractive index of n=0.90n = 0.90n=0.90, you can calculate the speed of light in this material using the same formula:v=cnv = \frac{c}{n}v=nc​v=3.00×108 m/s0.90=3.33×108 m/sv = \frac{3.00 \times 10^8 \, \text{m/s}}{0.90} = 3.33 \times 10^8 \, \text{m/s}v=0.903.00×108m/s​=3.33×108m/s

So, the speed of light in this hypothetical material would be approximately 3.33×1083.33 \times 10^83.33×108 m/s.

Summary:

  • The speed of light in water is approximately 2.26×1082.26 \times 10^82.26×108 m/s.
  • The speed of light in diamond is approximately 1.24×1081.24 \times 10^81.24×108 m/s.
  • The speed of light in Plexiglas is approximately 1.99×1081.99 \times 10^81.99×108 m/s.
  • The refractive index for a substance with a speed of 2.1×1082.1 \times 10^82.1×108 m/s is 1.431.431.43.
  • The refractive index for a substance with a speed of 1.5×1081.5 \times 10^81.5×108 m/s is 2.002.002.00.
  • The speed of light in a hypothetical material with a refractive index of 0.900.900.90 is approximately 3.33×1083.33 \times 10^83.33×108 m/s.

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