Amateur photographers cannot help but browse through Amazon.com for hours altogether looking for the biggest telephoto at the smallest price. Hours are spent debating the demerits of a Mirror lens versus the price of a Sigma 150-500mm lens or god forbid – the Canon L Series!. The question is, do you even need the 500mm telephoto? Or is it a must have before your trip to Africa?
The answer lies in a simple mathematical equation involving one multiplication and one division.
Before we delve into the maths, you need to keep in mind the following:
- Lenses do not perform their best at the extreme levels of Aperture and Focal Length. For ex: A lens with aperture 1.4 – 16 will produce soft images at f.4 and f16. It’s sharpest images are likely to be at two stop smaller than maximum. i.e. f2.8. Similarly, a 70-300mm telephoto zoom lens will produce slightly soft/distorted images at 70mm and 300mm focal lengths. So either buy a telephoto lens with a range higher than your requirement or use other techniques such as smaller aperture and tripod support to achieve sharper images.
- The more the telephoto range, the bigger the front element and the smaller the aperture. In plain English, telephoto lenses have big glass elements, hence they are heavy. Also, as the focal length increases, the aperture decreases to maintain sharp focus and thus light falling on the sensor decreases. As a result, you need to shoot with slower shutter speeds and take care to avoid image blurring.
- Research in optical photography technologies has resulted in evolution of new generation of lenses capable of performance similar to theoretical expectations. In plain english, throw enough money and you can buy high quality lenses (such as Canon L series) which give you terrific focal length as well as large apertures.
The ground being set, let us proceed.
In mathematical terms, the focal length (F) required is dependent on the distance of the object from lens, the height/width of the actual object and desired height/width of the image formed on the sensor.
- F = (distance x height of image) / height of object
- F = (distance x width of image) / width of object
Case Study: Kid at soccer game – Calculate Required Focal Length on an APS-C
Assuming that you are photographing with a Nikon D5100, which has an APS-C sized sensor (23.6 mm wide x 15.6 mm high). Your kid is four feet tall (1219.2 mm). The soccer pitch is 70 m wide and you are sitting near the boundary. You want to take shot when your kid is near the center line (distance from you = 35 m or 35000 mm). Let us also assume that in the frame, you want to allow for a little background and do not want to frame the shot very tightly, i.e. your kid’s head and feet are not near the edge of the frame, a fair bit of the playground is visible.
Since we are primarily working with height (kid is 1219.2 mm high), let us assume that you will frame the shot such that he will occupy 75% of the height of the image. i.e. 11.7 mm (75% of 15.6 mm, the height of the APS-C sensor)
Applying the formula: F = (35000 mm x 11.7 mm) / 1219.2 mm = 335 mm. Hence you need a telephoto lens that does at-least 335 mm (perhaps the Sigma 150 – 500mm?)
Crop Factor Adjustment: While the formula recommends a 300 mm lens, the D5100 user should actually buy a 200 mm lens. Why? Because a lens marked 200 mm produces an image equivalent to 300 mm on the Nikon D5100 (1.5x Crop Factor).
You could use a smaller telephoto lens. In that case, your kid’s image in the frame will be smaller and more of the background will be visible.
Case Study: Parrot on tree – Buy a Bigger Lens or Walk Closer to Subject?
Assuming that you are photographing with a Nikon D5100, which has a APS-C sized sensor (23.6 mm wide x 15.6 mm high). The parrot is 8 inches high (203.2 mm) and the branch it is sitting on is approximately 40 feet away (assuming the distance from you to base of tree. Ideally, we should also consider the height of the branch and use trigonometry to arrive at accurate distance, but I promised to keep this simple). Also, we want to frame very tightly and want the parrot to fill 90% of the height of the image (14.04 mm).
Applying the formula: F = (12192 mm x 14.04 mm) / 203.2 mm = 842.4 mm.
Even after adjusting for Crop Factor (842.4/1.5 = 561.6 mm), clearly you need a huge telephoto lens. Conventional lenses providing this range are pretty expensive; costing thousands of dollars. Mirror lenses (aka reflex lenses) with focal doubler (for ex: Opteka 500mm mirror lens with 2x Tele-convertor) are a possibility, but mirror lenses tend to be quite dim (aperture fixed at f8, f16 with tele-convertor), require very careful manual focusing and require sturdy tripods due to long exposures times.
Lets us consider that you are willing to risk your life and limb (from being attacked by a parrot) and approach the parrot so that is now only 10 feet (3048 mm) away.
Applying the formula: F = 3048 x 14.04 / 203.2 = 210.6 mm. This is well within the realm of a 70-300mm Telephoto lens. Perhaps you should step back a little and stop threatening the parrot.
Case Study: Crocodile at zoo – Calculate Shot Feasibility on a Point & Shot
Assuming that you are carrying a Point & Shoot camera like the Canon SX40 HS (featuring 24mm – 840mm equivalent range i.e. adjusted for Crop Factor), you are at the zoo and want to take a photograph of this African crocodile lazing in the sun.
The crocodile is about 15 feet (4572 mm) long (hardly any height to consider) and about 50 feet (15240mm) away from you. You want a tightly framed shot. The question is can you get the shot you want?
Let us find out.
The Canon SX40 has a typical Point & Shoot sensor size of 1/2.3″ (6.2 mm wide x 4.6 mm high). Since the crocodile is far longer that it is higher, we are bothered about the width of the object rather than height. Let us fill 95% of the width of the sensor (5.89 mm) with the crocodile.
Applying the formula: F = 15240 x 5.89 / 4572 = 19.63 mm.
Since the Canon is only 24 mm at it’s widest, you will have step back or the crocodile will not fit.
Assuming that you stepped back to 75 feet (22860mm) distance, applying the formula:
F = 22860 x 5.89 / 4572 = 29.45 mm. Now you are well within the range of your camera.
Note that focal length values quoted for Point & Shoot cameras are already adjusted for the huge crop-factor, hence no further adjustments are required for the formula.
Case Study: In Africa, face to face with lazing lion – Image Size / Ideal Distance Calculation on a Full Frame
More often than not, we purchase the equipment first (because of monetary limitations) and then worry about what we can photograph with it.
Assuming that you bought the excellent Canon 5D Mark II full-frame DSLR (sensor size: 36 mm wide x 24 mm high). You also splurged on the Sigma 150 – 500mm lens. Now you are in Africa, sitting in the Guide’s Jeep, about 100 feet (30480 mm) away from a Lion and wondering what sort of an image you are gonna get.
Note that the formula F = (distance x width of image) / width of object, can also be interpreted as:
Width of Object in Image = (Focal Length x Width of Object) / Distance to Object
Assuming we want a tight shot (95% of sensor width, 34.2 mm), the lion is approx 6 feet long (1828.8 mm) and we are applying the maximum telephoto of the lens, applying the formula:
Width of Object in Image = 500 mm x 1828.8 mm / 30480 mm = 30 mm. That’s 86% of the sensor width! Not bad at all.
We can also arrive at the distance required to shoot using another interpretation of the same formula:
Distance from Object = Focal Length x Width of Object / Width of object in Image
If we want the Lion to fill the entire 36 mm sensor width, applying the formula:
D = (500 mm x 1828.8 mm) / 36 mm = 25400 mm = 83.33 feet. That’s closer to the lion by 17 feet!
Note that Crop Factor of a Full Frame camera is 1.0. Hence no further adjustment is required to the formula.
Till Then, Stay Safe:
You will realize that arriving at what telephoto lens you need, or what distance you need to shoot from or simply what can you realistically expect from your lens is only a matter of multiplying and dividing. The formulas illustrated here were invented centuries ago. How I wish camera manufacturers either included a calculator function in the modern day cameras or at-least threw in a cheap one that could be stored in the camera bag and fished out when you desperately need, to arrive at the distance between you and an angry lion, based on size of the lion in the image you just shot.
Best Selling DSLR Cameras
- Nikon D7000: [amazonproduct=B0042X9LCO]
- Nikon D5100: [amazonproduct=B004V4IWKG]
- Nikon D3100: [amazonproduct=B003ZYF3LO]
- Canon 60D: [amazonproduct=B0040JHVC2]
- Canon 600D: [amazonproduct=B004J3V90Y]
Best Selling Lenses for Nikon cameras (Canon mount/equivalent also available)
- Tamron 18-270mm f/3.5-6.3 for all-purpose photography: [amazonproduct=B004FN1W28]
- Nikon 50mm f/1.8G for portrait photography: [amazonproduct=B004Y1AYAC]
- Sigma 150-500mm f/5-6.3 for wildlife photography: [amazonproduct=B001542X64]
- Tamron 90mm f/2.8 for Macro photography: [amazonproduct=B00021EE4U]
- Sigma 10-20mm f/3.5 for Wide-angle photography: [amazonproduct=B002D2VSD6]