What is the distance between an object and its real image formed by a thin converging lens with focal length f = 14 cm, if the object distance is 60 cm? (b) What is the minimum object-image distance for a real image formed by that lens?

To find the distance between an object and its real image formed by a thin converging lens, we can use the lens formula:

1/f = 1/v - 1/u,

where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens.

(a) Given that the object distance u is 60 cm and the focal length f is 14 cm, we can rearrange the formula to solve for the image distance v:

1/v = 1/f + 1/u

Substituting the values:

1/v = 1/14 + 1/60

To simplify the calculation, we can find the common denominator of 14 and 60, which is 420:

1/v = (30/420) + (7/420)
= 37/420

Taking the reciprocal of both sides:

v/1 = 420/37

Simplifying:

v = 11.35 cm

Therefore, the distance between the object and its real image formed by the lens is approximately 11.35 cm.

(b) The minimum object-image distance for a real image formed by a lens is when the object is at the focal point of the lens. In this case, the focal length f is 14 cm. As the object must be placed on the same side as the real image, the minimum object-image distance is simply twice the focal length:

Minimum object-image distance = 2 * f
= 2 * 14 cm
= 28 cm

Therefore, the minimum object-image distance for a real image formed by the lens is 28 cm.