Question

The refractive index of diamond is given as 2.42. A ray of yellow light of wavelength 589 nm passes through a rectangular diamond block in 1.32×10−9 s. What is the thickness of the block?

10.5 cm
12.7 cm
16.4 cm
22.3 cm

Answer 1

Answer on Question #52738-Physics-Optics

The refractive index of diamond is given as 2.42. A ray of yellow light of wavelength 589 nm passes through a rectangular diamond block in $1.32 \times 10^{-9}$ s. What is the thickness of the block?

- 10.5 cm

- 12.7 cm

- 16.4 cm

- 22.3 cm

Solution

The speed of yellow light with wavelength $\lambda = 589$ nm in diamond is

$$v = \frac{c}{n} = \frac{3.00 \cdot 10^{8} \frac{m}{s}}{2.42} = 1.24 \cdot 10^{8} \frac{m}{s}.$$

The thickness of the block is

$$d = vt = 1.24 \cdot 10^{8} \frac{m}{s} \cdot 1.32 \cdot 10^{-9} \, s = 16.4 \, \text{cm}.$$

Answer: 16.4 cm.

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