Quiz 25: Optical Instruments
The magnification of a magnifier depends upon the near point of the person and the focal length of the lens. A magnifier forms an enlarged, upright and virtual image of an object at or inside the focal point of the lens. A lens with short focal length can be used to get high magnifications and so an enlarged virtual image. Here the person will be observing the object across a room with the object being at large distances and the image being observed at a small distance from the lens. So the magnitude of the magnification of the lens would be less than one. Hence, the person will not be using the lens as a magnifier.
Use the relation between focal length, diameter, and f - number of the lens to solve for the f - number of the lens. The expression which relates focal length, diameter, and f - number of the lens is, Here, f is the focal length of the lens, and D is the diameter of the lens. Substitute 28 cm for f , and 4.0 cm for D in the equation to solve for . Therefore, the f - number of the lens is .
A laser beam is incident at a shallow angle on a horizontal machinist's ruler that has a finely calibrated scale and this engraved rulings on the scale give rise to a diffraction pattern on a vertical screen as shown in the below figure. Figure (a) shows the diffraction pattern produced by a laser light incident on scale. Figure (a) Light from the laser beam is nearly parallel to the horizontal ruler will scatter from ruler marks, which are separated by a distance apart to produce a diffraction pattern on a vertical wall at a distance away. The condition for constructive interference is, Here, The figure (a) includes two triangles. Redraw the first triangle as shown below. From above figure, the sin angle is, From the second triangle, the tan angle is, For a small angle . Then above equation changes as, Substitute for and for in equation . Substitute for in equation and solve for . Since and are measurable, the wavelength of the laser beam can be calculated by measuring the height of the bright spots as .