Relevant equations:

 = length of microscope tube

 = focal length of objective

 = focal length of eyepiece

 = linear magnification of objective

 = angular magnification of eyepiece

 = total magnification of microscope

Given:

Step 1: Plug the expression for  into the equation for total magnification, .

Step 2: Rearrange to isolate the unknown, 

Step 3: Plug in given quantities, taking the absolute value to find the magnitude of .

Relevant equations:

= angular separation of sources, in radians

 = wavelength of light emitted by sources, in meters

 = diameter of telescope

Step 1: Rearrange equation to isolate the unknown, :

Step 2: Plug in the given numbers for wavelength and angular separation:

The first thing to consider when answering this question is the fact that real images are always inverted and virtual images are always upright. Once you have determined one or the other, two answer choices can be eliminated.

The first equation that is necessary for this question is  .

From this we can determine that  is equal to . Since  is a positive number we know the image is real, and thus inverted.  

The second equation to consider is for magnification:  .

If the absolute value of  is greater than one, the image is magnified, and if the value is less than one, it is minimized.

We would expect the image to be minimized.  

In nearsightedness, the person cannot see far objects due to increased refraction. This causes the image to be formed in front of the retina. This condition is corrected using a diverging lens to compensate for the "over refraction" by the deformed cornea.

Relevant equations: 

Step 1: Plug in the given focal length and object distance to find the image distance:

Step 2: Find the magnification and orientation of the image:

A negative magnification means the image is inverted, and therefore real. A magnification smaller than 1 means the image is smaller than the object. 

The following result is true, in general, for converging lenses: if the object is outside , then the image is inverted, real, and smaller than the object.

This question deals with an application of optics. In this case we have a farsighted person and a near sighted person. The farsighted person would use a convex lens, which is a converging lens. This would allow all of the rays of light to converge on a single point, allowing them to heat the object up and start a fire. Wendy’s glasses are diverging lenses, which would cause the rays to separate.

The angle of reflection is the angle between the reflected light ray and a line perpendicular to the interface between the two media. The angle of reflection must be complementary to 20^o.

90^o – 20^o = 70⁰

This question is asking us about the different processes that can happen to light upon hitting a surface. Thinking back to the properties of light, we know that absorption, reflection, and refraction are all processes that light can undergo when interacting with a surface.

Absorption means that the energy associated with the light is captured, and no photons are ejected from the surface after the collision of the incident photon and the surface. Reflection occurs when no light enters the new medium and instead bounces off at the angle to normal that it hit. Refraction occurs when some light enters the new medium. In this case, light is entering glass from the air; thus, the process we are concerned about is refraction. 

For all waves, the angle of incidence is equal to the angle of reflection. The projection is to the opposite side of the normal at the same angle as the incident wave.

Think of the wall as a mirror. The angle with which the wave impacts a mirror will be equal to the angle with which it is reflected, but mirrored across the normal.

Since the index of refraction is 1.5, we can determine the speed of light in the glass using the following equation:

Rearranged to solve for velocity:

Once the speed of light in the glass is known, we can use this quantity to determine how long it will take for the light to travel the width of the glass .