Spherical Lenses

Step 1: Understanding the power of a lens.
The power of a lens is related to its focal length by the formula: where is in meters and is in diopters (D).

Step 2: Analyzing the given power.
For a lens with power , we can calculate the focal length : The negative sign indicates that the lens is a concave lens.

Step 3: Conclusion.
The correct answer is:

(A) is a concave lens

(D) has a focal length of -50 cm.

When dealing with lenses, the lens formula is given by: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. For a concave lens, the focal length is negative. Here, f = -10 cm, and the object is placed at the focus, hence u = -10 cm (object distances are also negative in lens equations).

Substituting in the lens formula: 1/(-10) = 1/v - 1/(-10). Simplifying gives:

1/(-10) = 1/v + 1/10

Bring similar terms together:

1/v = 1/(-10) - 1/10

1/v = -1/10 - 1/10 = -2/10 = -1/5

Thus, v = -5 cm. The negative sign confirms that the image is virtual and forms on the same side as the object.

To determine the best resolution of a confocal microscope using 500 nm light, we use the formula for resolution limit, also known as the Abbe diffraction limit: d = λ / (2NA), where d is the resolution, λ is the wavelength of light used, and NA is the numerical aperture of the objective lens. Assuming a commonly used numerical aperture for confocal microscopes is around 1.4, we calculate:

d = 500 nm / (2 × 1.4) = 500 nm / 2.8 ≈ 178.57 nm

Therefore, the best resolution is approximately 180 nm.