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.

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

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

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.

Using the lens formula, 1/f = 1/v - 1/u. Here, v = 40 cm, u = -20 cm. Solving gives f = 10 cm.

A positive focal length indicates that the lens is a convex lens, which converges light rays.

Power (P) is given by P = 1/f (in meters). Thus, f = 1/P = 1/2 = 0.5 m.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), n2 = 1.5, i = 30 degrees. Solving gives r = 19.2 degrees.

Using Snell's law, n1 * sin(theta1) = n2 * sin(theta2). Here, n1 = 1 (air), n2 = 1.5 (glass), and theta1 = 30 degrees. Thus, sin(theta2) = (1 * sin(30))/1.5 = 0.333, giving theta2 ≈ 19.1 degrees.

When a light ray passes through the center of curvature, it strikes the mirror perpendicularly, resulting in an angle of reflection of 0 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, sin(r) = (1 * sin(45)) / 1.5 = 0.471, giving r ≈ 28 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), n2 = 1.5 (glass), i = 60 degrees. Solving gives r = 40 degrees.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1 (air), θ1 = 30 degrees, n2 = 1.5. Thus, sin(θ2) = (1 * sin(30))/1.5 = 1/3, giving θ2 ≈ 20 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Thus, sin(r) = (1 * sin(30))/1.5 = 0.333, giving r ≈ 18.4 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), n2 = 1.5 (glass), i = 45 degrees. Solving gives r = 30 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1, n2 = 1.5, i = 30 degrees. Solving gives r ≈ 18.4 degrees.

When a ray passes through the center of curvature, it strikes the mirror perpendicularly, resulting in an angle of reflection of 0 degrees.

When a ray of light passes through the center of curvature, it strikes the mirror perpendicularly, resulting in an angle of reflection of 0 degrees.

A ray of light passing through the optical center of a lens continues in a straight line without bending.

According to the law of reflection, the angle of reflection is equal to the angle of incidence, which is 30 degrees.

According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is 30 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). For air (n1=1) and water (n2=1.33), we find r = 45 degrees.

Power (P) is given by P = 1/f (in meters). Thus, P = 1/0.2 = +5 D.

Using the lens formula, 1/f = 1/v - 1/u, we find v = 30 cm, meaning the image is formed 30 cm on the opposite side.

Using the lens formula, 1/f = 1/v - 1/u. Here, f = 15 cm, u = -30 cm. Solving gives v = 10 cm.

When the object is at the focus of a concave mirror, the rays are parallel after reflection, resulting in no image being formed.

Using the formula for minimum deviation, D = (n - 1)A. Here, n = √3 and A = 60 degrees. Thus, D = (√3 - 1) * 60 degrees, which approximates to 30 degrees.