Geometrical Optics - SS2 Physics Past Questions and Answers - page 3

Object distance (u) = -30 cm

Focal length of converging lens (f1) = 15 cm

Focal length of diverging lens (f2) = -20 cm

To find the final image distance (v), we can use the lens formula:

1/f1 = (1/v) - (1/u1),

1/f2 = (1/v) - (1/u2).

Since the image formed by the converging lens serves as the object for the diverging lens, the object distance for the diverging lens (u2) is the negative of the image distance formed by the converging lens.

u2 = -v1.

Substituting these values into the lens formula, we have:

1/15 = (1/v) - (1/-30),

1/-20 = (1/v) - (1/-v1).

Simplifying the equations, we get:

1/v = 1/15 + 1/30,

1/v = 1/20 - 1/v1.

Now, we solve the first equation for 1/v:

1/v = 2/30 + 1/30 = 3/30,

1/v = 3/30,

v = 30/3 = 10 cm.

Substituting the value of v into the second equation, we have:

1/10 = 1/20 - 1/v1.

To isolate 1/v1, we rearrange the equation:

1/v1 = 1/20 - 1/10 = 1/20 - 2/20 = -1/20.

Taking the reciprocal of both sides, we get:

v1 = -20 cm.

Since the image distance v1 is negative, the final image formed by the diverging lens is a virtual image.

Therefore, the final image distance is -20 cm, and it is a virtual image.

A compound microscope consists of two converging lenses, an objective lens, and an eyepiece. The objective lens forms a magnified real image of the object, which is further magnified by the eyepiece to produce a final virtual image. The working principle is based on the refraction of light at the lenses.

Compound microscopes have various applications in scientific research, medicine, and industry. They are widely used in biological research to observe and study microscopic organisms and cellular structures. In medicine, they are used for diagnosing diseases, examining tissue samples, and analysing blood cells. In industrial settings, they are used for quality control and inspection of small components and materials.