Optics Homework 2 (From Lynn)

What is the primary model used for understanding light in geometrical optics?

Geometrical model

What is the unit of measurement for vergence?

Diopters

How is vergence defined?

The reciprocal of the distance from the point source or image point to the reference point

What is the vergence of parallel rays of light?

Zero

What is the vergence of light rays that are converging?

positive

What is the vergence of light rays that are diverging?

Negative

What is the relationship between distance (l) and vergence (L) on air?

L=1/l

If an object is placed 0.5 meters in front of a lens, what is its object vergence?

-2.0D

What is the formula for image vergence (L')? (Vergence Relationship Formula)

L'=L+F

If an object vergence (L) is -3.0 D and the lens power (F) is +5.0 D, what is the image vergence (L')?

+2.0D

What type of image is formed when the image vergence (L') is positive?

Real Image

What type of image is formed when the image vergence (L') is negative?

Virtual image

What is the sign convention for distances measured to the left of the refracting surface?

Negative

What is the sign convention for heights measured above the optical axis?

Positive

What is the relationship between object distance (l), image distance (l'), and secondary focal length (f) for a thin lens on air?

1/l'-1/l=1/f'

What is the magnification (M) formula in terms of object and image distances?

M=(nl')/(n'l)

If an object is 10 cm high and the magnification (M) is 2, what is the height of the image?

20cm

What is the primary focal point (F) of a lens?

The point where parallel rays of light (going in the opposite direction as the one the lens is actually used on the problem) converge or appear to diverge after passing through the lens

What is the secondary focal point (F') of a lens?

The point where light rays that are initially parallel converge after passing through the lens

How does a converging lens affect parallel rays of light?

It converges them to a point

What is the vergence (L) of an object placed 1 meter in front of a lens?

-1.0D

What is the vergence (L') of an image located 0.25 meters behind a lens?

+4.0D

Calculate the power of a single refractive surface with an index of 1.5 and a radius of +12.5 cm that is surrounded by air?

4.0D

What is the formula for calculating image vergence (L') in terms of image distance (l') on air?

L'=1/l'

What happens to vergence (L) as the distance (l) increases?

it decreases

What is the paraxial approximation?

The approximation that angles are small enough that sin(θ) ≈ θ

In the paraxial approximation, what happens to the angle θ?

It is measured in radians

What is the vergence relationship formula for an optical system?

L'=L+F

What is the lateral magnification (M) formula in terms of object height (h) and image height (h')?

M=h'/h

If an object height (h) is 5 cm and the image height (h') is 10 cm, what is the magnification (M)?

2

What is the primary use of the paraxial approximation in optics?

To simplify calculations involving small angles

What does the sign convention for object distances state?

Distances to the left of the refracting surface are negative and distances to the right of the refracting surface are positive

What does the sign convention for image distances state?

Distances to the right of the refracting surface are positive and distances to the left of the refracting surface are negative

What is the relationship between the secondary focal length (f) and the power (F) of a lens?

F=n'/f' (in meters)

What type of lens has a positive focal length (f)?

Converging lens

What type of lens has a negative focal length (f)?

Diverging lens

What is the effect of a lens with a focal length of -0.5 meters on light rays?

Diverges them

What is the relationship between vergence (L), object distance (l), and refractive index (n)?

L=n/l

What is the image vergence (L') for an object located 0.25 meters in front of a lens with a power (F) of +4.0 D?

0.0D

What is the significance of the principal planes in an optical system?

They simplify the analysis of complex systems by allowing equivalent lenses to be used

How is lateral magnification (M) related to the object and image distances (l and l')?

M=l'/l

What is the effect of a lens with a higher index of refraction on the focal length?

Decreases the focal length

How is the focal length (f) of a lens affected by the curvature of its surfaces?

Increased curvature results in a shorter focal length

What happens to the image size created by a real object when it is moved closer to a converging lens; anywhere from - infinity to a distance still larger than F?

Images size increases

What happens to the image size if the object is moved further away from a diverging lens?

Image size decreases

What is the role of the principal planes in ray tracing?

They serve as reference planes to simplify calculations

How does the paraxial approximation affect the accuracy of optical calculations?

It provides a reasonable approximation for small angles

What is the relationship between the power (F) of a lens and its secondary focal length (f') in centimeters?

F = 100*n'/f'

What type of image is formed by a lens with a positive power (F)?

Real Image

What type of image is formed by a lens with a negative power (F)?

Virtual Image

How does the vergence (L) change as the distance (l) increases?

Vergence decreases

How is the focal length (f) of a lens affected by the refractive index (n)?

Higher refractive index results in a shorter focal length

How does the vergence (L) change as the distance (l) decreases? Vergence increases and tends towards infinity

What is the effect of moving the object further from the primary focal point of a diverging lens (further from the lens)?

The image becomes smaller and moves closer

What is the lateral magnification (M) of a lens if the object distance (l) is 0.5 meters and the image distance (l') is 1 meter?

2

How does increasing the positive power of a lens affect the position of an already real image?

It moves the image closer to the lens

What is the primary use of the paraxial approximation in optics?

To simplify calculations involving small angles

What does the sign convention for object distances state?

Distances to the right of the refracting surface are positive and distances to the left of the refracting surface are negative

What does the sign convention for image distances state?

Distances to the right of the refracting surface are positive and distances to the left of the refracting surface are negative

How is lateral magnification (M) related to the object and image distances (l and l')?

M= l'/l