# Can a Convex Lens Converge a Tilted Wavefront?

In summary, if a parallel beam of light with a varying speed travels through a glass slab with a linearly increasing refractive index, the wavefront will become tilted and the beam will no longer be parallel to the x-axis. This changes the direction of the beam and it may converge or diverge. Consequently, a convex lens with its principle axis along the x-axis may not be able to converge the rays at a focus. This is because there will be a path difference between two successive rays, which may result in interference. Furthermore, there may be a bright spot on a screen placed at the focal plane, but above the focus.
If I have a parallel beam of light parallel to x-axis, with the speed of light varying from bottom to top. Let it decrease from bottom to top. (To get such a beam one can pass the beam through a glass slab normal to its surface, whose refractive index increases linearly from bottom to top). Now although the beam is still parallel to x-axis, the wavefront is tilted. Will a convex lens (principle axis along x) be able to converge the rays at focus? There exists a path difference between two successes ice rays. Hence shouldn't we consider interference? Will there be a bright spot on a screen kept at focal plane but above the focus?

If I have a parallel beam of light parallel to x-axis, with the speed of light varying from bottom to top. Let it decrease from bottom to top. (To get such a beam one can pass the beam through a glass slab normal to its surface, whose refractive index increases linearly from bottom to top). Now although the beam is still parallel to x-axis, the wavefront is tilted. Will a convex lens (principle axis along x) be able to converge the rays at focus?

If the speed of the wavefront varies, then the beam of light will bend and change direction as it travels, possibly converging or diverging as well. It will no longer be parallel to the X-axis.

Drakkith said:
If the speed of the wavefront varies, then the beam of light will bend and change direction as it travels, possibly converging or diverging as well. It will no longer be parallel to the X-axis.
Actual reason: From huygens principle, direction of velocity is perpendicular to wavefront. Hence direction changes.

## What are wave fronts?

Wave fronts are imaginary surfaces that represent the continuous motion of a wave. They are perpendicular to the direction of the wave's propagation and are used to visualize how a wave moves through space.

## What is a convex lens?

A convex lens is a type of lens that is thicker in the middle and thinner at the edges. It is curved outwards and causes light rays to converge, meaning they come together at a single point known as the focal point.

## How do wave fronts interact with convex lenses?

When a wave front passes through a convex lens, the curvature of the lens causes the wave front to bend or refract. This is due to the change in speed of the wave as it moves through the lens. The resulting wave front is then focused at a point known as the focal point.

## What is the focal length of a convex lens?

The focal length of a convex lens is the distance between the lens and its focal point. It is an important characteristic of a lens as it determines how much the lens will bend incoming light rays. The longer the focal length, the less the lens will bend the light.

## What is the difference between a convex lens and a concave lens?

A convex lens is thicker in the middle and causes light rays to converge, while a concave lens is thinner in the middle and causes light rays to diverge. This means that a convex lens produces a real, inverted image, while a concave lens produces a virtual, upright image.

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