F-number lengths. Therefore, reduced–depth-of-field effects will require smaller f-numbers when using small-format cameras than when using larger-format cameras. Image sharpness is related to f/number through two different optical effects: aberration, due to imperfect lens design, and diffraction which is due to the wave nature of light. The blur optimal f-stop varies with the lens design. For modern standard lenses having 6 or 7 elements, the sharpest image is often obtained around 5.6–8, while for older standard lenses having only 4 elements (Tessar formula) stopping to 11 will give the sharpest image. The larger number of elements in modern lenses allow the
Standard 52-card deck jokers, often distinguishable with one being more colorful than the other, are added to commercial decks, as some card games require these extra cards. Modern playing cards carry index labels on opposite corners or in all four corners to facilitate identifying the cards when they overlap and so that they appear identical for players on opposite sides. The most popular standard pattern of the French deck is sometimes referred to as "English" or "Anglo-American" pattern. It has been shown that because of the large number of possibilities from shuffling a 52-card deck, it is probable that no two fair card