Geometrical Optics - SS2 Physics Past Questions and Answers - page 2

The laws of refraction describe the behaviour of light as it passes from one medium to another. The first law states that the incident ray, the refracted ray, and the normal to the interface between the two media all lie in the same plane. The second law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media. Mathematically, this can be expressed as Snell's Law: n₁sinθ₁ = n₂sinθ₂, where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.

These laws are essential in understanding the behaviour of light when it enters a different medium. For example, when light passes from air to water, it undergoes refraction due to the change in speed. This is why a straw appears to bend when partially submerged in a glass of water.

Lenses are transparent optical devices that can bend or refract light to form images. There are two primary types of lenses: convex lenses and concave lenses. Convex lenses are thicker in the middle and thinner at the edges, while concave lenses are thinner in the middle and thicker at the edges.

Convex lenses have properties such as converging light rays and forming real or virtual images. They are commonly used in magnifying glasses, telescopes, and cameras to produce magnified and clear images. On the other hand, concave lenses have properties such as diverging light rays and producing virtual images. They are used in devices like eyeglasses to correct nearsightedness or myopia.

Lenses have properties such as focal length, which determines the distance between the lens and the image formed, and power, which measures the ability of a lens to bend light. These properties play a crucial role in various practical applications, such as in corrective lenses for vision correction, microscope objectives for magnification, and camera lenses for focusing and capturing high-quality images.

Focal length (f) = 10 cm

Object distance (u) = -20 cm (negative sign indicates the object is placed in front of the lens)

1/10 = 1/v - 1/-20

1/10 = (20 - v) / (20v)

20v = 10(20 - v)

20v = 200 - 10v

30v = 200

v = 200 / 30

v ≈ 6.67 cm

Focal length (f) = -15 cm (negative sign indicates a diverging lens)

Object distance (u) = 30 cm

Using the lens formula, 1/f = 1/v - 1/u, we can find the image distance (v).

1/(-15) = 1/v - 1/30

To simplify the equation, we can take the common denominator:

-2/30 = (30 - v) / (30v)

Now, we can cross-multiply and solve for v:

-2v = (30 - v) x 30

-2v = 900 - 30v

28v = 900

v = 900 / 28

v ≈ 32.14 cm

The image distance (v) is approximately 32.14 cm.

To calculate the magnification (M), we can use the formula M = -v / u, where M represents the magnification.

M = -(32.14) / 30

M ≈ -1.07

The magnification is approximately -1.07.

Therefore, the image distance is approximately 32.14 cm and the magnification is approximately -1.07.