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    43.

    A lens has a focal length 'f'. Derive the lens maker's formula, relating f to the refractive index 'n' of the lens material and the radii of curvature R1R_1 and R2R_2 of its surfaces.

    A

    1f=1R1+1R2\frac{1}{f} = \frac{1}{R_1} + \frac{1}{R_2}

    B

    1f=(nβˆ’1)(1R1+1R2)\frac{1}{f} = (n-1)(\frac{1}{R_1} + \frac{1}{R_2})

    C

    1f=(nβˆ’1)(1R1βˆ’1R2)\frac{1}{f} = (n-1)(\frac{1}{R_1} - \frac{1}{R_2})

    D

    f=(nβˆ’1)(1R1βˆ’1R2)f = (n-1)(\frac{1}{R_1} - \frac{1}{R_2})

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    45.

    A rocket in space ejects gas at a constant rate ΞΌ\mu kg/s with a constant speed vev_e relative to the rocket. If the initial mass of the rocket is M0M_0, what is its velocity after time tt?

    A

    ΞΌvet\mu v_e t

    B

    veΞΌtM0v_e \frac{\mu t}{M_0}

    C

    veln⁑(M0M0βˆ’ΞΌt)v_e\ln(\frac{M_0}{M_0 - \mu t})

    D

    veln⁑(M0βˆ’ΞΌtM0)v_e\ln(\frac{M_0 - \mu t}{M_0})

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