Using Snell's law, sin(θ2) = sin(60)/1.5, we find θ2 = 30 degrees.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1 (air), θ1 = 45 degrees, n2 = 1.5 (prism). Solving gives θ2 ≈ 30 degrees.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.33/2.42) ≈ 36.9°.

Since the angle of incidence (60°) is greater than the critical angle (approximately 41.8° for glass to air), total internal reflection occurs.

To determine if total internal reflection occurs, we first find the critical angle using sin(θc) = 1/n = 1/1.5, which gives θc ≈ 41.8°. Since 60° > 41.8°, total internal reflection will not occur.

Critical angle θc = sin⁻¹(1/2.42) ≈ 24.4°.

For a prism, the angle of minimum deviation (D) can be approximated as D = A for small angles, thus D = 60 degrees.

Using the lens formula, 1/f = 1/v - 1/u; here, f = 15 cm and u = -30 cm. Thus, 1/v = 1/15 + 1/30 = 1/10, giving v = 10 cm.

According to the law of reflection, the angle of reflection equals the angle of incidence.

Using the lens maker's formula, f = R/2(n-1). Here, R = 10 cm, n = 1.5, so f = 10/(2(1.5-1)) = 10/1 = 10 cm.

Using the lens maker's formula, f = R/(n-1) = 30/(1.5-1) = 30/0.5 = 60 cm.

Using the lens maker's formula, the focal length is calculated to be 15 cm.

Using the lens formula, 1/f = 1/v - 1/u, we find v = 8 cm.

For a concave lens, the image formed is virtual and erect when the object is placed beyond the focal length.

For a concave lens, the image formed is virtual and erect when the object is placed at any distance.

Using the lens formula, the image distance is calculated to be -16.67 cm.

Using the mirror formula, 1/f = 1/v + 1/u, where f = -10 cm (concave mirror), u = -30 cm. Solving gives v = -15 cm, which means the image is formed 15 cm in front of the mirror.

Using the mirror formula, 1/f = 1/v + 1/u. Here, f = -5 cm (concave mirror), u = -10 cm. Solving gives v = -10 cm.

Power (P) = 1/f (in meters). f = 0.15 m, so P = 1/0.15 = +6.67 D.

Using the lens formula 1/f = 1/v - 1/u, we find v = 30 cm.

Using the lens formula 1/f = 1/v - 1/u, we find v = 60 cm.

Using the lens formula 1/f = 1/v - 1/u, where f = 20 cm and u = -40 cm, we find v = 20 cm. The image is formed at 20 cm on the opposite side.

Power (P) = 1/f (in meters). f = 20 cm = 0.2 m, so P = 1/0.2 = 5 D.

Critical angle θc = sin^(-1)(1/n) = sin^(-1)(1/2.42) ≈ 24.4°.

Using the lens formula 1/f = 1/v - 1/u, we have 1/(-10) = 1/v - 1/5. Solving gives v = -3.33 cm.

Using the lens maker's formula, R = 2f(n-1) = 2*10*(1.5-1) = 20 cm.

Using the lens maker's formula, f = R/(n-1), we find f = 20/(1.5-1) = 40 cm.

For total internal reflection to occur in a fiber optic cable, the core must have a higher refractive index than the cladding.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.4/1.5) ≈ 42.0°.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.5/1.6) ≈ 38.7°.