What is the velocity ( in cm/s) of image wrt a stationary observer in situation shown in the figure. Object and mirror move towards right with velocities of 10 cm/s and 2 cm/s respectively.
What is the velocity ( in cm/s) of image wrt a stationary observer in situation shown in the figure. Object and mirror move towards right with velocities of 10 cm/s and 2 cm/s respectively.
We have developed the formula for the velocity of the image with respect to the mirror by considering the fact that the mirror formula is always valid from the mirror frame of reference (ie. Considering mirror to be at rest).
We get,
−−−→vi,m=−−−→cvo,m(Where c=f2(f−u2)).....(1)Here. we have to solve from the ground frame of reference so, we will use;−−−→vi,m=→vi−−→vm & −−→vo,m=→vo−−→vmSubstituting above values of −−→vi,m & −−→vo,m in equation (1) we get,→vi=−−−→−cvo+(c+1)−−→vm,Now in this problem,u=−10cmf=10cmSo we get,c=14Also,→vo=10cmsAnd,−→vm=2cmsPutting these values in our formula,We get,
→vi=(−14×10)+(54×2)=0.Hence we get image speed to be 0.
We have developed the formula for the velocity of the image with respect to the mirror by considering the fact that the mirror formula is always valid from the mirror frame of reference (ie. Considering mirror to be at rest).
We get,
−−−→vi,m=−−−→cvo,m(Where c=f2(f−u2)).....(1)Here. we have to solve from the ground frame of reference so, we will use;−−−→vi,m=→vi−−→vm & −−→vo,m=→vo−−→vmSubstituting above values of −−→vi,m & −−→vo,m in equation (1) we get,→vi=−−−→−cvo+(c+1)−−→vm,Now in this problem,u=−10cmf=10cmSo we get,c=14Also,→vo=10cmsAnd,−→vm=2cmsPutting these values in our formula,We get,
→vi=(−14×10)+(54×2)=0.Hence we get image speed to be 0.
