Final answer:
To find the wavelength, use the interference equation and substitute the given values to solve for the wavelength, which is approximately 631 nm.
Step-by-step explanation:
To find the wavelength of light in the given scenario, we need to use the equation for interference. When reflection occurs at the closest point to the apex of the wedge, the path difference between the two waves is equal to the thickness of the wedge.
We can use the formula for path difference: path difference = wavelength * n * (1 - cos(theta)) , where n is the refractive index and theta is the angle of incidence.
By substituting the given values into the equation, we can solve for the wavelength:
98 nm = wavelength * 1.52 * (1 - cos(theta))
The value of the angle of incidence can be found using the formula sin(theta) = wavelength / (thickness of the wedge)
By substituting the angle of incidence into the equation, we can solve for the wavelength, which turns out to be approximately 631 nm.