### Related Problems with Solution

##### Problem 1 : Dispersion Through a Glass Prism

**Problem Statement:**
A ray of white light enters a glass prism at an angle of 45° to the base of the prism. The refractive index of the glass is (1.5). Calculate the angle of deviation for the violet component of the light when it exits the prism.

##### Solution :

**Step 1:**Given values: Angle of incidence θ_{1}= 45 °,Refractive index ((n)) = (1.5).**Step 2:**Use Snell’s Law to find the angle of refraction θ_{2}inside the prism: $$(n_1\sin\theta_1 = n_2\sin\theta_2),$$ where n_{1}is the refractive index of air.**Step 3:**Calculate $$(\theta_2): (1.0 \cdot \sin(45^\circ) = 1.5 \cdot \sin(\theta_2)).$$**Step 4:**Solve for $$(\theta_2): (\sin(\theta_2) = \frac{1}{1.5}).$$**Step 5:**Calculate $$(\theta_2): (\theta_2 = \sin^{-1}\left(\frac{1}{1.5}\right)).$$**Step 6:**Calculate the angle of deviation δ using the prism formula: $$(\delta = A + \epsilon - \alpha),$$ where (A) is the angle of the prism, ε is the angle of deviation, and α is the angle of incidence inside the prism.**Step 7:**Substitute the values: $$(\delta = 60^\circ + \epsilon - 45^\circ).$$**Step 8:**Solve for $$(\epsilon): (\epsilon = \delta - 15^\circ).$$

So, the angle of deviation for the violet component of light is $$(\delta - 15^\circ).$$