Compound microscope: The distance between the object and the eyepiece of a compound microscope is 18.0 cm. The focal length of its objective lens is 0.80 cm and the eyepiece has a focal length of 2.3 cm. The near-point distance of the person using the microscope is 25.0 cm. What is the total overall magnification of the microscope?

Lens-maker’s formula: A double-concave lens has equal radii of curvature of

Capacitors in combination: Three capacitors are arranged as shown in the figure. C1 has a capacitance of 5.0 pF, C2 has a capacitance of 10.0 pF, and C3 has a capacitance of 15.0 pF. Find the voltage drop across the entire arrangement if the voltage drop across C2 is 311 V.

Electric field and potential: In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x2y2 + yz3 – 2z3x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).

Eyes: A machinist with normal vision has a near point at 25 cm. The machinist wears eyeglasses in order to do close work. The power of the lenses is +1.75 diopters. With these eyeglasses, what is the near point of the machinist?

Compound microscope: The objective and the eyepiece of a microscope have focal lengths of 4.00 mm and 25.0 mm, respectively. The objective produces a real image 30 times the size of the object. The final image is viewed at infinity, and the near point of the microscope user is at 25.0 cm. What is the distance between the object and the focal point of the objective?

Eyes: The near point of a person’s uncorrected eyes is 125.0 cm and the far point is at infinity. What is the focal length of a contact lens that will move the near point to 25.0 cm from this person’s eyes?

Eyes: The near point of a farsighted person’s uncorrected eyes is 80 cm. What power contact lens should be used to move the near point to 25 cm from this person’s eyes?

Force on parallel wires: A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure). Which of the following statements is true?

Energy in an inductor: At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing?