Since the mirror is concave, the focal point will be in front of the mirror. The focal length is equal to one half of the radius of curvature.



R_c is the radius of curvature. Plugging in 0.85m for R_c allows us to solve for the focal length.

0.43m is equal to 43cm.

The refractive index of a medium (n) is equal to the speed of light (c) divided by the velocity of light through the medium (v).

Rearranging the equation allows us to see the relationship regarding v.
 
The lower the refractive index, the faster the velocity of light. Medium A has the smaller refractive index. Light will travel faster through medium A at a velocity equal to the speed of light divided by the refractive index.

Solve for frequency by taking the inverse of the period.

Next, solve for wavelength by dividing velocity by frequency.

The beat frequency is simply the difference between two frequencies.

We are given the frequency of each tuning fork, so we can use the equation to solve for the beat frequency.

Right away you can rule out the answers with units in seconds, as the unit of frequency is an inverse second, or Hz. Frequency is measured in cycles per second. If eight crests pass a given point in fifteen seconds, the frequency is given by the number of crests divided by the time period.

First calculate the frequency of the wave (cycles/sec). The problem tells us that there are ten cycles in 1.6s.

Next find the period by taking the inverse of the frequency.

Finally, find the wavelength by dividing the velocity by the frequency.

The light portion of the electromagnetic spectrum, from lowest to highest frequency, is red, orange, yellow, green, blue, indigo, violet (ROYGBIV).

Frequency is proportional to temperature, and wavelength is inversely proportional to frequency. Since the energy level corresponds with the temperature, objects that emit a higher frequency and shorter wavelength photon will have higher energy. This corresponds with violet, as it is the highest frequency (shortest wavelength) of visible light

The Doppler shift equation for light is , where f is the source frequency, f' is the observed frequency, v is the relative velocity between source and observer, and c is the speed of light.

When the source and observer are moving closer together, v is positive, so the observed frequency is greater than the source frequency. Greater frequency also implies shorter wavelength, so visible light is shifted towards the blue end of the spectrum.

As Einstein determined, light has properties of both a particle and a wave. In the particle sense, it has mass, velocity, and momentum. The wave property of light allows for diffraction, and constructive and destructive interference. For the MCAT, it is important to know that the photon (the particle of light) has both particle and wave properties. In fact, all objects have both particle and wave properties; however, their wave property becomes less obvious with increasing mass.

The frequency of light does not change when it enters a medium with a different index of refraction; in this case, that new medium is the glass of the prism. From the velocity of light equation we know the relationship between velocity and frequency.

v is the velocity of light,  is the wavelength, and f is the frequency. When light enters the prism, its velocity changes due to the new index of refraction, but its frequency remains constant.

Because the frequency does not change, we can see that velocity is directly proportional to wavelength; thus, the shorter the wavelength, the slower the velocity. So both wavelength and velocity change when frequency is constant.