🔍 انكسار الضوء والعدسات

"Refraction of light: a change in the direction of wave propagation when the wave moves from one medium to another."

When refraction occurs, the wave speed changes.

The wavelength changes when refraction happens.

The incident and refracted waves come from the same source, so the frequency remains constant.

Write the correct number for each item based on the diagram:

When does light refract toward the normal? When does it refract away from the normal? And when does no refraction occur?

Explore how light bends when traveling between two different media. Change the refractive indices and the angle of incidence and observe the results:

Snell (1621) found that when light passes from one transparent medium to another, the sines of the angles satisfy:

where \(n_1\) is the refractive index of medium 1, \(n_2\) of medium 2, \(\theta_1\) the angle of incidence, and \(\theta_2\) the angle of refraction.

When light goes from air (n=1) to water (n=1.33) with an incidence angle of 30°:

The refractive index is the ratio of the speed of light in vacuum to its speed in a medium:

It has no unit (it is a ratio) and is typically greater than or equal to 1.

Note: Values are typically measured at 20°C and a wavelength of 589 nm.

In this simulation, change the media, incidence/refraction angles, and refractive indices, then apply Snell’s law and verify the equality:

In this external simulation, change the refractive index using the slider on the right and calculate the refractive index and the angle at which the ray emerges:

Send light from a medium with a higher refractive index to one with a lower refractive index, and compare the incidence and refraction angles.

Increase the incidence angle until the refraction angle reaches 90° — that incidence angle is called the critical angle \(\theta_C\).

There are two main types of lenses:

Thicker at the center and thinner at the edges. It converges light rays: parallel rays refract and meet at a single point called the focus (a real focus).

Thicker at the edges and thinner at the center. It diverges parallel rays; however, the extensions of the refracted rays meet at a point called the focus (a virtual focus).

First, we must know the principal rays in lenses (all rays obey the law of refraction):

It refracts through the focus in a convex lens; in a concave lens, its extension passes through the focus.

It continues straight without deviation.

In a convex lens (or whose extension passes through the focus in a concave lens), it refracts parallel to the principal axis.

In this simulation, place an object at different distances from a convex or concave lens, draw the resulting image, and determine its properties:

Complete the ray diagrams based on the previous simulation when the object is placed at different positions in front of a convex lens. Then check the solution:

Now complete the diagrams for a concave lens: at which object position does the image look the same? Then check the solution:

Using similar triangles, we can derive the main lens equations (as with mirrors).

Thin lens equation:

where \(X_o\) is the object distance, \(X_i\) the image distance, and \(f\) the focal length.

Important: the sign convention (positive/negative) must be applied correctly depending on lens type and image type.

In optics, we use positive and negative signs to indicate the positions of objects and images relative to a lens. The table below summarizes the sign conventions:

Practical tip: apply signs only to the quantities that are known for the specific case.

Magnification is the ratio of image height \(h_i\) to object height \(h_o\); it also equals the negative ratio of image distance to object distance:

Note: the sign of magnification is always opposite to the sign of the image distance.

In this simulation: move the blue circle above the object to change its position. Move the circle at the focus to change the focal length. Drag the blue circle to the right side of the lens to switch it into a concave lens.

Each time, change the object position and record the focal length and object distance, then calculate the image distance and magnification.

Chromatic aberration is an image distortion caused by a lens's inability to focus different colors at the same point, because the refractive index depends on wavelength (color).

Glass typically refracts blue light more than red light, so different colors converge at different points.

Spherical aberration is an optical effect seen in lenses and mirrors because rays near the edge bend (or reflect) more than rays near the center.

The aberration grows as the ray approaches the lens/mirror edge, so rays focus at different points along the principal axis instead of a single focus; parabolic surfaces are used instead of spherical ones in telescopes to reduce this distortion.