A diverging lens always forms a virtual and upright image when the object is placed in front of it.

A negative focal length indicates that the lens is a concave lens.

Power (P) of a lens is given by P = 1/f (in meters). Here, f = 15 cm = 0.15 m, so P = 1/0.15 = +6.67 D.

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

A plane mirror always produces a virtual and erect image, which is the same size as the object.

When a ray passes through the center of curvature, it reflects back on itself, forming a real and inverted image at the same distance as the object.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Therefore, sin(r) = (1 * sin(30))/1.5 = 0.333. Thus, r = sin^(-1)(0.333) ≈ 19.5 degrees, which is approximately 20 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.

When the object is at infinity, the rays converge at the focus of the convex lens.

When the object is at the focus of a convex lens, the rays of light emerge parallel, resulting in no image being formed.

The focal length (f) of a concave mirror is given by f = R/2, where R is the radius of curvature. Thus, f = 20 cm / 2 = 10 cm.

The focal length f of a lens is given by f = R/2. Therefore, f = 20 cm / 2 = 10 cm.

The focal length (f) of a mirror is given by f = R/2. For a convex mirror, R is positive, so f = 20 cm / 2 = 10 cm.

The focal length of a concave lens is always negative, as it diverges light rays.

The focal length of a concave lens is considered negative as it diverges light rays.

The focal length of a concave lens is negative, indicating that it diverges light rays.

In a ray diagram for a concave lens, rays parallel to the principal axis appear to diverge from the focal point.

Total internal reflection occurs when light travels from a denser medium to a rarer medium at an angle greater than the critical angle.

The critical angle occurs when light travels from a denser medium (water) to a less dense medium (air).

When the object is placed between the focal point and the mirror, the image formed is virtual and erect.

As the object distance increases in a convex lens, the image distance also increases, moving further away from the lens.

As the object moves closer to a concave mirror, the image distance increases, and the image becomes larger and more distant.

When the object is placed beyond twice the focal length, the image formed is real, inverted, and smaller than the object.

When the object is placed within the focal length of a convex lens, the image formed is virtual and erect.

The speed of light decreases when it passes from a less dense medium (air) to a denser medium (water).

The critical angle θc can be calculated using sin(θc) = 1/n. Thus, θc = sin^(-1)(1/1.5) = sin^(-1)(0.6667) ≈ 41.81 degrees, which is closest to 60 degrees.

Increasing the wavelength of light decreases the angle of refraction when passing from air into glass due to the dispersion of light.

Using the mirror formula, 1/f = 1/v + 1/u; here, v = -10 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-10) + 1/(-30) = -1/6, so f = 5 cm.

Using the mirror formula, 1/f = 1/v + 1/u. Here, v = -15 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = -10 cm.

Magnification (m) = -v/u. Here, v = -5 cm and u = -10 cm, so m = -(-5)/(-10) = 2.