The Thickness of the Ozone Layer Can Be Estimated Using $\ln I _ { 0 } - \ln I = k x \sec \theta$

Multiple Choice

The thickness of the ozone layer can be estimated using the formula $\ln I _ { 0 } - \ln I = k x \sec \theta$ where I ₀ is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and $6$ is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 $x$ 10 ^{- 8} centimeter with k $$\mathbb { N }$$ 1.93, I _o /I is measured as 1.72 and $\theta = 12 ^ { \circ }$ . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.

A) $x = 0.27$ cm
B) $x = 0.51$ cm
C) $x = 0.26$ cm
D) $x = 0.29$ cm
E) $x = 0.30$ cm