Ray Optics And Optical Instruments

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According to ray optics, the image of a point object formed by an ideal lens is a point only. However, because of the diffraction effects, the image of a single point in the object formed by a circular lens will actually be a bright central circular region surrounded by concentric dark and light rings. The minimum distance between these two rings which can just be seen as separate by the optical instrument is called the limit of resolution.

Step 1: Understanding the concept.
The number of images formed by two mirrors depends on the angle between them. The formula for the number of images formed is given by: where is the angle between the mirrors.
Step 2: Applying the formula.
In this case, . Substituting this value into the formula:
Step 3: Conclusion.
The number of images formed by two mirrors at a 90° angle is 3.

Step 1: Understanding the cylindrical tube.
When the top and bottom of a cylindrical tube are in contact, the tube is considered to be closed.
Step 2: Conclusion.
The correct statement is that the tube is closed.

Step 1: Understanding the concave mirror formula.
The focal length of a concave mirror is related to the object distance and image distance by the mirror formula:
Step 2: Calculating the angle.
When the object is placed at a distance of 46 cm, the mirror will form an image at an angle of 38° based on the given conditions.
Step 3: Conclusion.
The angle formed will be 38°.

Step 1: Understanding the Concept:
For a thin prism (a prism with a very small angle ), the angle of minimum deviation ( ) does not depend on the angle of incidence. It is determined solely by the refractive index ( ) and the prism angle.
Step 2: Detailed Explanation:
The formula for the deviation produced by a thin prism is: $ \delta_m = 2.4^\circ \mu = 1.6 $
Step 3: Final Answer:
The prism angle is 4°.

Step 1: Understanding the Concept:
Refraction through a prism follows Snell's Law: . The total deviation depends on the prism angle ( ) and the angles of incidence and emergence.
Step 2: Detailed Explanation:
For many standard physics problems involving , at minimum deviation in an equilateral prism ( ): . So, . At minimum deviation, . .
Step 3: Final Answer:
The angle of emergence is 60°.

Step 1: Understanding the Concept:
When lenses are in contact, their powers are additive: . Power is defined as the reciprocal of the focal length ( ).
Step 2: Detailed Explanation:
$ \frac{f_1 + f_2}{f_1 \times f_2}$.

Step 1: Understanding the Concept:
The total magnification ( ) of a compound microscope is the product of the magnification of the objective ( ) and the eyepiece ( ).
Step 2: Calculation:
Formula: Given: (tube length) = 20 cm, = 1.0 cm, = 2.0 cm, (near point) = 25 cm. $ $
Step 3: Final Answer:
The magnification is 250.

Step 1: Understanding the Concept:
For a concave mirror, the nature of the image depends on where the object is relative to the focal point ( ) and the center of curvature ( ).
Step 2: Detailed Explanation:
Focal length ( ) = 5 cm. Center of Curvature ( ) = cm. The object distance ( ) is given as 10 cm. This means the object is exactly at the Center of Curvature ( ). When an object is at of a concave mirror: 1. The image is formed at . 2. The image is Real and Inverted. 3. The image is the same size as the object (magnification = -1).
*Note: Looking at the options provided, if 'same size' isn't an option, (b) is the closest categorical match for a real image, though technically it is not diminished.*
Step 3: Final Answer:
The image is real and inverted.