# Exercise 1. – Focal length and angle of view

Taking the first steps with OCA includes numerous exercises. These are great help to get to know the camera better, understanding focal length, angle of view, focusing on still and moving subjects with different speed and aperture.

Focal length is the distance between the lens and the sensor when the lens focused at infinity measured in mm, the angle of view is the amount of a scene that a lens can take in measured in degrees. A 50 mm lens is considered to be a standard lens for a 35 mm film camera as it produces an image that through the human eye would be recognized as normal and not distorted in any way. According to the manual my Canon 60D camera has a smaller sensor of  22.3 x 14.9 mm, compared to full frame size of  36 x 24 mm which means my Sigma 30 mm 1.4  Art lens becomes 48 mm as a result of 1.6 crop factor.

To calculate the ‘actual’ effective angle of view I use Pythagoras’ Theorem to determine the longest side (i.e. the diagonal length or hypotenuse) of a right-angled triangle. Pythagoras’ Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. A^2 + B^2 = C^2, where “C” is equal to the length of the hypotenuse and “a” and “b” are the lengths of the other two sides. (22.3 x 22.3)  + (14.9 x 14.9) = C^2 497.29 + 222.01 = C^2 719.3 = C^2 C = 26.82 mm is the length of the diagonal of the 60D sensor. Therefore the diagonal measurement of the full frame sensor is 43.3 mm compare to the cropped sensor’s 26.82 mm 43.3 / 26.82 = 1.61 actual crop factor.

For this exercise I used my Canon 60D with 15-85 mm f/3.5-5.6 IS USM lens and a tripod, I shot in Raw from the bridge over River Wharfe in Ilkley, West Yorkshire and processed the images in Lightroom.

15 mm, f/ 3.5, 1/1000, ISO 200

29 mm, f/ 4.5, 1/400, ISO 200

85 mm, f/ 5.6, 1/320, ISO 200

I took the exposure information from Lightroom’s metadata panel. I printed these images onto A4 paper with my Canon IP4600 photo printer, I noticed that the colours are different on the screen, I made some adjustments but it didn’t work, I have to calibrate properly.

I went back to the same spot, the top of the bridge and I noticed that if I hold the second picture approx 0.5 m away from me it will appear the closest to my eye, 29 mm x 1.6 crop factor resulting 46.6 mm,  however I could have done better because it was still slightly further than what I have actually seen from there. Looking at my first picture taken at 15 mm wasn’t too comfortable, I hold that approx 25 cm away from my eyes. I could not hold the third one as far as I needed to because of the limitation of the space but studying the first and the second picture helped me to understand how focal length works with different size of sensors and how it appears to the human eye. I also realized I haven’t paid attention to aperture, I should have shot with few stops smaller (larger number) to get a sharper image.