Suppose the near point of your eye is \(2.0 \cdot 10^{1} \mathrm{~cm}\) and the far point is infinity. If you put on -0.20 diopter spec tacles, what will be the range over which you will be able to see objects distinctly?

We are given the power of the spectacles as P = -0.20 diopters. Using the definition of power, we can find the focal length f: $$f = \frac{1}{P} = \frac{1}{-0.20 \mathrm{D}} = -5 \mathrm{m}$$ The negative focal length indicates that the spectacles are concave lenses.

To find the new near point, we need to consider the object distance (u) as the original near point, which is given as \(2.0 \cdot 10^{1} \mathrm{~cm}\). The new image distance (v) will be formed closer to the eye, which means the person can now see more distinctly objects closer than before. Using the lens formula: $$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$ Plug in the values of f and u: $$\frac{1}{-5 \mathrm{m}} = \frac{1}{2.0 \cdot 10^{1} \mathrm{~cm}} + \frac{1}{v}$$ Convert the object distance to meters: $$\frac{1}{-5 \mathrm{m}} = \frac{1}{0.2 \mathrm{m}} + \frac{1}{v}$$ Solve for v: $$\frac{1}{v} = \frac{1}{-5 \mathrm{m}} - \frac{1}{0.2 \mathrm{m}} = -\frac{1}{4 \mathrm{m}}$$ $$v = -4 \mathrm{m}$$ The negative sign indicates that the new image is formed on the same side as the object. Since it's the minimum distance for distinct vision, we can ignore the negative sign. Therefore, the new near point is \(4 \mathrm{m}\).

To find the new far point, we need to consider the object distance (u) as infinity, as the original far point is infinity. In this case, the new image distance (v) will be equal to the focal length of the lens. For the spectacles, we have already calculated the focal length as f = -5m. Since the new image distance (v) should be equal to the focal length, we have: $$v = -5 \mathrm{m}$$ As the new far point should be a positive distance, we can use the concept of the negative sign indicating an object and image on the same side of the lens. Therefore, the new far point is 5 meters.

Now that we have calculated the new near point and the new far point, we can find the range of vision over which a person can see objects distinctly with the given spectacles. The range of vision can be found by simply subtracting the new near point from the new far point: $$\text{range} = \text{new far point} - \text{new near point} = 5 \mathrm{m} - 4 \mathrm{m} = 1 \mathrm{m}$$ #Conclusion# With the -0.20 diopter spectacles, the person will be able to see objects distinctly within the range of 1 meter, between 4 meters and 5 meters from their eye.