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

Power (P) = 1/f, so f = 1/P = 1/(-2) = -0.5 m = -50 cm.

A negative power indicates a concave lens.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2), 1 * sin(60°) = 1.33 * sin(θ2) => sin(θ2) = (sin(60°)/1.33) ≈ 0.577, θ2 ≈ 35.0°.

Since the angle of incidence (70°) is greater than the critical angle (approximately 41.8°), total internal reflection occurs.

The critical angle for diamond to air is sin⁻¹(1/2.42) ≈ 24.4°. Since 70° > 24.4°, total internal reflection will occur.

The intensity of the central maximum is greater than that of the other maxima in a diffraction pattern.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). 1 * sin(30°) = 2 * sin(θ2) => sin(θ2) = 0.25 => θ2 = 15°.

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

Using the grating equation d sin(θ) = mλ, where d = 1/1000 mm = 1 x 10^-6 m, for m=1, we find θ ≈ 30 degrees.

When the angle between the transmission axes of two polarizers is 90 degrees, no light passes through, resulting in zero intensity.

When the angle between the transmission axes of two polarizers is 90 degrees, no light is transmitted, resulting in zero intensity.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2), 1.5 * sin(45°) = 1 * sin(θ2) => sin(θ2) = 1.5 * 0.7071 = 1.0607, which is not possible, hence total internal reflection occurs.

Since 70° > θc = sin⁻¹(1/1.5) ≈ 41.8°, total internal reflection will occur.

Since the critical angle for glass to air is sin⁻¹(1.00/1.5) ≈ 41.8°, and 60° > 41.8°, total internal reflection occurs.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1.5, n2 = 1.0, and θ1 = 30°. Thus, sin(θ2) = (1.5 * sin(30°))/1.0 = 0.75, leading to θ2 ≈ 48.6°.

Since the angle of incidence (70°) is greater than the critical angle (approximately 41.8° for glass to air), total internal reflection occurs.

Critical angle θc = sin⁻¹(1/1.6) ≈ 38.7°. Since 70° > 38.7°, total internal reflection occurs.

The critical angle for glass to air is sin⁻¹(1/1.5) ≈ 41.8°. Since 70° > 41.8°, total internal reflection will occur.

When the angle of incidence equals the angle of refraction, it indicates that the light is passing from one medium to another of the same optical density, hence they are the same medium.

According to Snell's law, if the angle of incidence equals the angle of refraction, the light is traveling in the same medium, which can be vacuum or air.

At the critical angle, the angle of refraction is 90°, meaning the refracted ray travels along the boundary.

When the angle of incidence equals the critical angle, the light ray is refracted along the boundary at 90°, marking the threshold for total internal reflection.

The refractive index n can be calculated using n = 1/sin(θc). For θc = 30°, n = 1/sin(30°) = 1/0.5 = 2.00.

Using the formula n = 1/sin(θc), where θc = 45°, we find n = 1/sin(45°) = 1/0.7071 ≈ 1.41.

Image distance (v) = Object distance (u) + Distance between object and image = 30 cm + 70 cm = 40 cm.

Increasing the distance between the slits decreases the fringe width, as fringe width is inversely proportional to the slit separation.

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

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 10 cm = 20 cm.

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.