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 is given by D = A(n - 1), where A is the angle of the prism. Here, D = 60(1.5 - 1) = 30 degrees.

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.

According to the law of reflection, the angle of reflection equals the angle of incidence, so it is 60 degrees.

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, the focal length is calculated to be 20 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.

Concave lenses always produce virtual and upright images regardless of the object distance.

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 = 30 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.

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

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.