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When the final image in a compound microscope is formed at infinity, the angular magnification due to the eyepiece ($m_e$) is given by:

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Explanation

From NCERT Eq. 9.44(b): 'When the final image is formed at infinity, the angular magnification due to the eyepiece is $m_e = (D/f_e)$'.

In a compound microscope, if the objective lens has a focal length $f_o = 1.0$ cm, and the eyepiece has a focal length $f_e = 2.0$ cm, with a tube length $L = 20$ cm, the total magnification (for image at infinity) will be approximately:

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Explanation

Using the formula $m = m_o m_e = (L/f_o)(D/f_e)$, and typical $D = 25$ cm: $m = (20/1.0)(25/2.0) = 20 imes 12.5 = 250$. This matches the example calculation in the NCERT.

Why is it difficult to make the focal length of lenses in a microscope much smaller than 1 cm?

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Explanation

While not explicitly stated as the only reason for the 1cm limit, the NCERT mentions: 'In practice, it is difficult to make the focal length much smaller than 1 cm. Also large lenses are required to make L large. ... In modern microscopes, multi-component lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses.' The difficulty in minimizing focal length below 1 cm is related to managing aberrations and manufacturing practical, high-quality optics.

For best viewing through a compound microscope, why should the eye be positioned a short distance away from the eyepiece, rather than on it?

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Explanation

The NCERT (Q 9.25 (e)) implies this by asking 'Why? How much should be that short distance between the eye and eyepiece?'. The 'eye-ring' concept (exit pupil) is where all the rays from the object converge after passing through the eyepiece, and placing the eye there provides the largest field of view without vignetting.

What is the effective focal length of two thin lenses of focal lengths $f_1$ and $f_2$ placed in contact?

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Explanation

The formula for lenses in contact is $1/F = 1/f_1 + 1/f_2$, which simplifies to $F = f_1f_2 / (f_1 + f_2)$.

Which of the following describes the fundamental nature of heat transfer by convection?

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Explanation

The NCERT text states, 'Convection is a mode of heat transfer by actual motion of matter.' This distinguishes it from conduction (molecular vibration) and radiation (electromagnetic waves).

Convection primarily occurs in which states of matter?

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Explanation

The NCERT text specifies, 'It is possible only in fluids.' Fluids include both liquids and gases because their particles are free to move and can undergo bulk transport required for convection.

Which of the following is an example of natural convection?

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Explanation

The NCERT text states, 'Natural convection is responsible for many familiar phenomena... creating a sea breeze near a large body of water.' The other options are explicitly mentioned as examples of forced convection.

In natural convection, when a fluid is heated from below, why does the heated part rise?

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Explanation

The NCERT text explains, 'When a fluid is heated from below, the hot part expands and, therefore, becomes less dense. Because of buoyancy, it rises and the upper colder part replaces it.'

Which of the following processes primarily involves forced convection?

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Explanation

The NCERT text explicitly states, 'In the human body, the heart acts as the pump that circulates blood through different parts of the body, transferring heat by forced convection and maintaining it at a uniform temperature.'

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