For reflected light in air, the wavelength and speed remain $589\,\text{nm}$ and $c=3.0\times10^8\,\text{m s}^{-1}$. The frequency is $\nu=c/\lambda=(3.0\times10^8)/(589\times10^{-9})=5.09\times10^{14}\,\text{Hz}$. In refraction into water, frequency is unchanged. The speed becomes $v=c/n=3.0\times10^8/1.33=2.26\times10^8\,\text{m s}^{-1}$, and the wavelength becomes $\lambda_w=\lambda/n=589/1.33=443\,\text{nm}$.
(a) Reflected light: wavelength $589\,\text{nm}$, frequency $5.09\times10^{14}\,\text{Hz}$, speed $3.0\times10^8\,\text{m s}^{-1}$. (b) Refracted light: wavelength $443\,\text{nm}$, frequency $5.09\times10^{14}\,\text{Hz}$, speed $2.26\times10^8\,\text{m s}^{-1}$.
A point source sends out spherical wavefronts. A point source at the focus of a convex lens emerges as a parallel beam, so the wavefront is plane. A distant star is so far away that the small portion of its spherical wavefront intercepted by the Earth can be treated as plane.
(a) Spherical. (b) Plane. (c) Approximately plane.
The refractive index is $n=c/v$, so $v=c/n=(3.0\times10^8)/1.5=2.0\times10^8\,\text{m s}^{-1}$. Glass is dispersive, so its refractive index depends on colour. Violet has a larger refractive index in glass than red, hence $v=c/n$ is smaller for violet light.
(a) $2.0\times10^8\,\text{m s}^{-1}$. (b) No. Violet light travels slower than red light in a glass prism.
For bright fringes, $x_n=n\lambda D/d$. Here $x_4=1.2\,\text{cm}=1.2\times10^{-2}\,\text{m}$, $d=0.28\,\text{mm}=2.8\times10^{-4}\,\text{m}$, $D=1.4\,\text{m}$ and $n=4$. Thus $\lambda=x_4d/(nD)=(1.2\times10^{-2})(2.8\times10^{-4})/(4\times1.4)=6.0\times10^{-7}\,\text{m}=600\,\text{nm}$.
$600\,\text{nm}$.
A path difference $\lambda$ corresponds to phase difference $2\pi$, so the point is a maximum and $K=4I_0$ for equal slit intensities. For path difference $\lambda/3$, the phase difference is $\phi=2\pi/3$. The intensity is $I=4I_0\cos^2(\phi/2)=4I_0\cos^2(\pi/3)=4I_0(1/4)=I_0=K/4$.
$K/4$.