What is Focal Length?
The Focal Length of a lens is the distance between the point of convergence in your lens and the image sensor or film plane in your camera when the lens is focused at infinity. (as shown in the image above, credits: expertphotography)
Different Sensor Sizes
Full Frame sensor and Cropped (APS-C) sensor are the two most widely used sensor sized in today’s digital cameras. The standard sensor size of a full frame sensor is 36 × 24 mm and that of a cropped sensor is 22.3 x 14.9 mm (Canon) and 23.6 x 15.7 mm (Nikon).
As you can clearly analyze from the sensor sizes mentioned above, a full frame image sensor produces an image of 36mm x 24mm, which is equivalent to the size of the 35mm film. This is the reason why this sensor is known as the full frame sensor.
As the cropped sensor is smaller in size, we have to multiply the focal length of the lens by the crop factor of the image sensor to get the correct angle of view. The crop factor of a cropped sensor on a Canon digital camera is x1.6 and x1.5 on a Nikon digital camera.
Understanding lens focal length on full frame and cropped sensors
You might still be of the perception that the focal length of the lens increases when it is mounted on a cropped sensor, for e.g. a 100mm lens would give a focal length of 150mm on a cropped sensor camera (Canon). Well, this is not entirely true.
The focal length of the lens remains 100mm only, but what changes is the angle of view.
One of the differences between the full frame and the crop sensor cameras is that the former provides a wider angle of view (as shown in Red) as compared to the latter (as shown in Blue).
But how exactly is the angle of view defined? Well, the angle view is determined by two factors: the focal length of the lens being used and the size of the sensor. This means that when using the same lens, both the formats will result in a different angle of view.
Let’s consider another scenario, while clicking photos on two different cameras installed with both the sensors using the 50mm lens, the full frame camera will give you the exact angle of view for which the lens has been designed. However, the cropped sensor camera will give you a narrower angle of view because of smaller sensor size.
To get the same angle of view on the crop sensor camera, you will have to use a lens with the focal length of 50mm/1.6 = 31.25mm.
On the other hand, if you want to get the same angle view of what you are getting on the crop sensor camera, you will have to mount a 50mm x 1.6 = 80mm lens on your full frame camera.
To get the same angle view on either of the sensors, use these simple rules:
Focal length of the lens on a full frame camera MULTIPLIED by the crop factor = Focal length of the lens on a crop sensor camera
Focal length of the lens on a crop sensor camera DIVIDED by the crop factor = Focal length of the lens on a full frame camera
The concept of Image Circle
Why do lens manufacturers design lenses for full frame and cropped sensors separately? The reason behind this categorization of lenses is the image circle. When you use a lens mounted on a camera (with a sensor of any size), the lens projects light in the shape of a circle onto the sensor.
The lenses are designed in such a manner that the diameter of the circle projected on the sensor is larger than the diagonal on the sensor frame. So on a full frame sensor (36x24mm) the lens would project an image circle larger than 43.2mm, and 26.81mm(Canon)/28.34mm(Nikon) on a cropped sensor.
This image above should also answer another question, why we get dark vignette effect while using the lens designer for a cropped sensor camera on a full frame camera.
The lens for cropped sensor produces smaller image circle (pink color), which if used on a full frame camera body, will produce dark vignette as no light is falling on the sensor beyond the image circle (pink color).
But if you use the lens designed for full frame camera on a cropped sensor, there would be no vignette effect as the image circle is wider than the sensor size and the complete sensor is receiving the light.