Question

Will the magnification produced by a simple magnifier increase, decrease, or stay the same when the object and the lens are both moved from air into water?

Short answer

Answer: The magnification produced by a simple magnifier will decrease when the object and lens are both moved from air to water.

Step-by-step solution

Know the lens formula for air and water

The lens formula relates the focal length (f), object distance (u), and image distance (v) in a medium. The lens formula is given by: (1/f) = (n-1)((1/R1) - (1/R2)), where n is the refractive index of the lens with respect to the medium, R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface. Since we are comparing the magnification when the lens and object are in air and water, we need to consider the lens formula in both media. In air, the refractive index is 1 while in water, it is greater than 1. We will use the refractive index (n) of the lens and water to find the new focal length in water.

Calculate the new focal length in water

To find the new focal length in water, we need to use the new refractive index (na = refractive index of lens in air, nw = refractive index of lens in water). The lens formula in water becomes: 1/fw = (na/nw - 1)((1/R1) - (1/R2)). Note that when the medium was air, the lens formula was: 1/fa = (na - 1)((1/R1) - (1/R2)). Divide the first equation by the second equation to get: fw/fa = (na - 1)/(na/nw - 1). Since na > 1 and nw > 1, fw > fa. The focal length in water is greater than the focal length in air.

Compare magnifications in air and water

We know that the magnification formula is M = (1 + D/f). Since the focal length in water (fw) is greater than the focal length in air (fa), the magnification in water will be less than the magnification in air. M_water = (1 + D/fw) < (1 + D/fa) = M_air. Therefore, when the object and lens are both moved from air to water, the magnification produced by a simple magnifier will decrease.