Two people look at the same object through the same microscope.Person A has a near point of x_np and person B has a near point of 2x_np.If person A sees the object magnified m times,with what magnification does person B see the object? A)m B)m/2 C)m/4 D)2m E)4m

Question

Quizplus · Accepted Answer

The magnification of a microscope is given by the formula M = f/object distance, where f is the focal length of the objective lens. Since both individuals are looking at the same object through the same microscope, the focal length is the same for both. Let the object distance be d. Then, for person A, the distance between the object and the lens is x_np + d, and for person B, it is 2x_np + d. Person A's magnification is given by M = f/(x_np + d). Person B's magnification is given by M = f/(2x_np + d). Dividing the two equations, we get: M_B/M_A = f/(2x_np + d) / f/(x_np + d) M_B/M_A = (x_np + d) / (2x_np + d) M_B/M_A = 1 / (2 - 1/(x_np + d)/(x_np)) Since m = M_A, we can substitute and simplify: M_B = m / (2 - 1/(x_np + d)/(x_np)) As d approaches infinity, the term (x_np + d)/(x_np) approaches 1, so the denominator approaches 1, and M_B approaches 2m. Therefore, the answer is D) 2m.

Two People Look at the Same Object Through the Same