All about visual angle This is the angle

All about visual angle This is the angle made by the top and bottom of the object being drawn in straight lines through the focal point of the eye. Let this be an eye This is the distance between eye and object Here is the height of an object in the world

More realistic eye diagram, showing the light going through the focal point of the lens, which helps focus the light on the retina, the sensitive surface on the back of the eye, made of receptors (rods and cones).

This angle And this angle Are the same, because they are formed by two lines intersecting.

This portion of the circumference is Called a visual arc. It is measured in the same units as the angle, and equals the value of the angle. Think of this as the amount of room taken up on the back of the eyeball by the image of the object being projected.

Numbers B H C A D Consider the right triangle, ABC Let H stand for the height of BC Let D stand for the Distance between AC and the focal point of the eye.

Numbers B H A C a D The ratio, “H divided by D, ” H/D, in a right triangle, is called the tangent of the angle, alpha, a.

Numbers B H C A D If H = 3 and D = 4, then the tangent = ¾, or. 75. What if we looked at a new object that is 1. 5 units in height at a distance of 2? Like this [new line in triangle] The ratio (tangent) stays the same.

Numbers B H C A D All lines that touch line AB at one end, and AC at the other end take up the same angle -- and the ratios will stay the same. This or even THIS

Crucial Point So far, we are showing the projections to the eye FROM THE SIDE. What is the person with the diagrammed eye SEEING? In terms of what is diagrammed so far, all 4 lines on the previous slide look the same! There is just a line going straight up and down for the distance of the angle. Make sure that this makes sense to you!!

Conversions We usually refer to the size of an angle, or its associated arc, in units called radians or units called degrees. Most of you will be more familiar with degrees. So far, we have calculated the tangent, which is specific to degrees and radians, but not the same unit. For today (Jan. 21, 2014), we go to our Excel sheet for the remainder of this exercise.