Which distance is associated with Knapp's law for achieving a retinal size magnification of 1?

Which distance is associated with Knapp's law for achieving a retinal size magnification of 1?

• A. 5 mm
• B. 10 mm
• C. 16.67 mm
• D. 25 mm

Answer: (C)

Knapp's law uses a simple eye model where the retinal image size is related to how large the object appears (its angular size) and the eye's focal length. The retinal image size is roughly f times the angular size, with the angular size being S/d for an object of size S at distance d. So the retinal magnification M is about S_ret/S ≈ f/d. To have a retinal magnification of 1, you set d equal to the focal length f. The human eye’s focal length is about 16.7 mm, so the distance that yields M = 1 is approximately 16.7 mm. That’s why the correct distance is around 16.67 mm. If the object is closer, M would be greater than 1; if farther, M would be less than 1.

Knapp's law uses a simple eye model where the retinal image size is related to how large the object appears (its angular size) and the eye's focal length. The retinal image size is roughly f times the angular size, with the angular size being S/d for an object of size S at distance d. So the retinal magnification M is about S_ret/S ≈ f/d. To have a retinal magnification of 1, you set d equal to the focal length f. The human eye’s focal length is about 16.7 mm, so the distance that yields M = 1 is approximately 16.7 mm. That’s why the correct distance is around 16.67 mm. If the object is closer, M would be greater than 1; if farther, M would be less than 1.