1.2 - Mathematical concepts

Question 1

Why are we interested in angles

Answer 1

• Angles subtended to our eye is important to the size things appear to be
• Knowing the angle is all we need to know to determine physical height it appears to be ( angles are independent of distance and physical size )

Question 2

Example of things different size but appear same size

Answer 2

Thumbnail and the car aren’t the same (physical) size! However, they appear the same size because they subtend the same angle at your eye
= Its possible to have objects of different physical sizes but can be presented at different distances and can appear same size when we look at them

Question 3

How can we use angles to determine height/image size

Answer 3

• Angles subtended by objects at our eyes fundamentally affect image size
• Letters presented at different distances can produce the same image height on the retina
• Knowing the angle is all we need to know to determine physical height it appears to be
  e. g. All E’s subtend same angle ( 5 min of arc ) = all appear same size

Question 4

Degrees, minutes and second

Answer 4

Minutes = ‘
Seconds = “
60mins of arc = 1 degree

Question 5

Small angle approximation:

Answer 5

• Tells us about ideal image formation
• When angles are small (they can still be several degrees or more) then we can approximate the trig functions sin(q) and tan(q) by the angle itself expressed in radians

Question 6

What unit is small angle approximation

Answer 6

Only radians

Question 7

How to convert between radians and degrees

Answer 7

Degree to radians: x π/180

Radians to degrees: x 180/π

Question 8

What is a geometric progression

Answer 8

Has a common ratio between successive numbers. For example the progression: 1, 2, 4, 8, 16, 32 has a common ratio of 2.

Question 9

What is the common logarithm of a number

Answer 9

· The common logarithm of a number is the exponent the number 10 is raised to.
· For example 102 = 100 therefore log10(100) = 2

Question 10

Why are logs important in vision

Answer 10

Because our eyes respond on a logarithmic scale to a number of stimuli.

Question 11

When are logs useful

Answer 11

· Useful when numbers have a large range of values:

· For example, the range of light levels our eyes respond to is 100,000,000 times. We can refer to this as 8 log units.