Reflection, Refraction, and Lenses

Light Rays as Models

Optics problems use rays to model the direction energy travels. A ray is not a physical string in space; it is a useful line showing the path of light. The Regents may show mirrors, lenses, glass blocks, water, or vehicle safety mirrors in public sampler-style contexts. Use those diagrams as evidence, then apply the optical rule.

The 2025 Physics Reference Tables include reflection, refraction, lens, and magnification relationships. The hard part is often not finding the formula. It is identifying the normal line, the medium change, and the image type.

Reflection

Reflection occurs when a wave bounces from a boundary. For a plane mirror, the law of reflection says theta_i = theta_r. Both angles are measured between the ray and the normal, not between the ray and the mirror surface.

If a ray makes a 30 degree angle with the mirror surface, it makes a 60 degree angle with the normal. The reflected ray also makes a 60 degree angle with the normal. This angle-measurement detail is a common trap.

A plane mirror forms a virtual, upright image that appears behind the mirror. The image is the same size as the object and the same distance behind the mirror as the object is in front. The light does not actually come from behind the mirror; the reflected rays only appear to originate there.

Curved Mirrors

Curved mirrors change the direction of reflected rays in a way that can converge or diverge light. Concave mirrors can form real images when the object is beyond the focal point. Convex mirrors spread reflected rays and form virtual upright images with a wider field of view.

For Regents reasoning, identify whether reflected rays actually meet. If actual rays converge, the image is real and can be projected on a screen. If rays only appear to come from a location, the image is virtual.

Refraction and Index of Refraction

Refraction is bending caused by a speed change as a wave enters a new medium. The reference tables give n = c/v, where n is absolute index of refraction and v is the speed of light in that medium. A larger n means a lower light speed in the material.

Snell's law is n1 sin theta1 = n2 sin theta2. Angles are again measured from the normal. When light enters a higher-index material at an angle, it slows and bends toward the normal. When it enters a lower-index material, it speeds up and bends away from the normal.

Frequency stays the same across the boundary because the source controls it. Speed and wavelength change. Since v = f lambda, a lower speed with unchanged frequency means shorter wavelength in the material.

Comparing Media in Exam Diagrams

If a diagram shows air, water, and glass, compare indexes before predicting the bend. Light has its greatest speed in air among those three simplified choices and usually its lowest speed in glass. A ray entering straight along the normal changes speed but does not bend sideways because there is no unequal path delay across the wavefront.

Total Internal Reflection

When light travels from a higher-index medium toward a lower-index medium, a large enough angle can produce total internal reflection. The light reflects inside the original medium instead of refracting out. Fiber-optic communication uses repeated internal reflection to guide light along a thin transparent strand.

The Regents may not require a critical-angle calculation every time. It may ask which condition allows the effect: light must start in the higher-index medium and strike the boundary at an angle larger than the critical angle.

Lenses and Principal Rays

A converging lens is thicker in the middle and can bring parallel rays toward a focal point. A diverging lens spreads parallel rays so they appear to come from a focal point on the same side as the object.

For a ray diagram with a converging lens, use principal rays: one parallel to the axis then through the far focal point, one through the center continuing straight, and one through the near focal point then parallel to the axis. Where rays meet, or appear to meet, gives the image.

A screen test helps classify the image. If a sharp image can form on a screen, the light rays really converge there and the image is real. If no screen can catch it and the image appears only by looking through or into an optical device, the image is virtual.

Lens Equation and Magnification

The reference tables give 1/F = 1/do + 1/di and hi/ho = -di/do. These equations use reciprocals, so do not subtract distances directly. If F = 8 cm and do = 24 cm, then 1/di = 1/8 - 1/24 = 2/24 = 1/12, so di = 12 cm.

Magnification connects image height to object height. A negative image height indicates inversion under the sign convention in the table relationship. A magnitude less than 1 means smaller; greater than 1 means larger.

Constructed-Response Optics Habits

Use a ruler for rays and label the normal at boundaries. If the prompt asks for an angle, state whether it is measured from the normal. For calculations, write the reciprocal setup before solving.

In explanation questions, connect the image or bending to the path of light. Say that the ray bends toward the normal because light slows in the higher-index material, or that the image is virtual because the rays only appear to meet behind the mirror or lens.

Optics rewards clean geometry. Most errors come from measuring from the surface, ignoring the medium order, or treating apparent ray extensions as real rays.