To solve the given problem, we’ll use the lens formula:

1. Distance of the object from the lens: The lens formula is given by: 1/f = 1/v – 1/u where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens.

Using the given information, we can calculate the distance of the object from the lens as follows: 1/10 = 1/30 – 1/u
Simplifying the equation, we have: 1/u = 1/10 – 1/30 1/u = (3 – 1)/30 1/u = 2/30 1/u = 1/15
Therefore, the distance of the object from the lens is 15 cm.

1. Size of the object: The magnification formula is given by: magnification (m) = v/u where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens.

Using the given information, we can calculate the magnification as follows: m = v/u 2/15 = 2cm/u
Cross-multiplying, we get: 2u = 2cm * 15 2u = 30cm u = 30/2 u = 15cm
Therefore, the size of the object is 15 cm.

1. Drawing a ray diagram for a compound microscope: A compound microscope consists of two lenses: the objective lens and the eyepiece lens. The objective lens forms a magnified real image, which is further magnified by the eyepiece lens to create a final magnified image. The following steps describe how to draw a ray diagram for a compound microscope:

Step 1: Draw the object (O) on the left side of the first lens (objective lens).
Step 2: Draw the first converging lens (objective lens) with a focal length (f1).
Step 3: Draw a dotted line for the principal axis, passing through the center of the lens.
Step 4: Draw a horizontal ray from the top of the object (O) parallel to the principal axis. After passing through the objective lens, this ray should bend towards the principal axis and go through the focal point (F1).
Step 5: Draw a ray from the top of the object (O) that passes through the optical center of the objective lens. This ray should continue straight without bending.
Step 6: After the rays pass through the objective lens, they will form a magnified real image (I) on the right side of the lens.
Step 7: Draw the second converging lens (eyepiece lens) with a focal length (f2). This lens is positioned to the right of the objective lens.
Step 8: Draw a dotted line for the principal axis of the second lens.
Step 9: Draw a horizontal ray from the top of the image (I) parallel to the principal axis. After passing through the eyepiece lens, this ray should bend towards the principal axis and go through the focal point (F2).
Step 10: Draw a ray from the top of the image (I) that passes through the optical center of the eyepiece lens. This ray should continue straight without bending.
Step 11: After the rays pass through the eyepiece lens, they will appear to emanate from the virtual image formed by the eyepiece lens. This will create a final magnified image that can be seen by the eye.
Note: The actual drawing of the ray diagram would require more precise measurements and scales, but this description provides a general idea of the steps involved